Which fighter jet is the safest outside of combat?
There are a number of barriers to labeling a single fighter as the "safest" - your proposed method is probably the best overall picture, but there are some barriers to even that.

Differences in use and training

Fighter aircraft are extremely complex and are asked to performed complex missions, even in training, where there may be little room for error. Due to the United States' huge military budget and wide-reaching foreign operations, US military pilots tend to have high flight time compared to many smaller countries, including other ones that fly US-produced aircraft. (Russia's modernization has led to increased flight time there, though still far below US or Cold War levels. China's modernization has pushed their training levels much closer to the US, as noted on p. 10 in this 2016 study ).

As pilot experience leads to decreased accident rate (to a point, at which accident rate goes up again even higher than inexperienced pilots), some of the air forces which fly very little likely have some contribution to a possible higher accident rate, irrespective of the safety of the aircraft they fly.

In addition, differences in philosophy of use from one country to another may lead to more dangerous employment - high speed low level flight is inherently more dangerous than flying high-altitude caps - and two air forces may utilize the same aircraft in such vastly different roles. This may lead to a fatal accident from a malfunction that at altitude, would be comparatively benign.

Lack of records

This is the biggest barrier, I think. Unlike commercial airliners, which worldwide predominately are produced by only two major manufacturers (Airbus/Boeing) and a handful of smaller regional-class producers, fighter aircraft are produced by a number of companies:


USA - Boeing, General Dynamics, Lockeed Martin
Sweden - Saab
Britain - BAE
Europe (multiple contributors) - Eurofighter GmbH
France - Dassault
Russia - UAC (combination of former companies Mikoyan, Sukhoi, Yakovlev, and others)
China - CAC, XAC, HAIC, Shenyang
India - HAL


While some of these aircraft are unique to a single country, many are used by multiple countries (e.g. for US-produced aircraft, numbers may be available for the US accident rates, but not for other countries). The F-16 has had 4,500+ aircraft produced, and is operated by 26 different countries on 5 continents. One difficulty with this, other than the difference in records is the number of different variants in service. As Mazura noted in a comment below, the F-35 has seen no fatal incidents in US service, but other countries have had incidents. 9 countries currently operate a F-35 variant, with at least 4 more countries planning to acquire the type. The MIG-29 has at least 24 current and 10 former operators spanning 5 continents as well. So great difficulty exists in retrieving fleet-wide numbers (in addition, as political situations change, it may make spare parts acquisition or maintenance more difficult, leading to major variances in reliability).

In addition, countries with smaller militaries that have traditionally relied on importing their military aircraft such as Japan, Israel, Turkey, Pakistan and Taiwan have produced or are developing indigenous fighters.

Due to the diverse nature of these countries that produce the aircraft - some of which are produced by somewhat state-owned companies, it makes the retrieval of records difficult.

Additionally, since Airbus and Boeing need private corporations to purchase their aircraft, and safety is a huge selling point (or rather, poor safety record is a major turn off) in selling tickets, then the easy retrieval of accident histories for airliner class aircraft is much more crucial than high-performance military aircraft.

Age of Fleets

Looking at probably the best kept public record producers,  The U.S. Air Force Safety Center has year-by-year and lifetime mishap histories for all current USAF fighters, but it doesn't separate out combat and non-combat incidents/fatalities. But when you compare the various US fighters:


A-10: 51 fatalities, 5.65 million hours (0.90/100,000 hours)
F-15: 44 fatalities, 6.80 million hours (0.65/100,000 hours)
F-16: 86 fatalities, 11.28 million hours (0.76/100,000 hours)
F-22: 1 fatality, 355 thousand hours (0.28/100,000 hours)
F-35: 0 fatalities, 96 thousand hours (0.0/100,000 hours)


But the F-22 has only been flying since FY2003, and the F-35 since FY2012, so comparing those to aging aircraft that have been around since the early 1970s doesn't paint an accurate picture. You can look at the 5-year and 10-year trends, however to see a more recent summary. For the USAF, the best rate would be the A-10, with no fatal accidents in the last 10 years, averaging 88,000 flight hours a year. Not unique to the USAF (indeed, all aviation sections of the US Military deal with this), many other countries have dealt with aging fleets as well, often due to the less frequent production of new designs since the cold war. (ex: Russia, Iran).

One note is that many combat aircraft in service with even the most modern air forces are no longer in production - the A-10 was last produced in 1984 and the MIG-31 in 1994, while some aircraft (like the MIG-29 and F-16) are still in production today.

Conclusion

Due to the barriers listed above, I think objectively calling a single fighter the "Safest" is likely an impossible task. But from the various characteristics, the safest record probably belongs to an aircraft that is flown by a country fairly regularly, leading to good experience in its pilots, possibly is employed predominately in an air-to-air role more regularly, and is produced more recently, yet long enough ago that the major design flaws in a new aircraft are worked through. I would say the best candidates would be the F-15E or the Eurofighter (which I found an article indicating 2 deaths in 240,000 flight hours across a diverse group of countries - Wikipedia indicates another 4 fatal crashes since then in an unknown amount of flight hours).