Using RJ10 connectors for other data than intended
This is acceptable. RJ10/RJ45/etc... are versatile and already used for multiple applications (phone, ethernet, RS-232, RS-485, CAN, whatever, ...), some of these applications being not really standardized, but commonly accepted. So you could add one more use of it without shocking people.

However, there are a few things to consider:


The current capacity is usually small. And the wire gauge of premade cables is also small. If you need more than 200/300 mA on a wire, this is a problem.
Cable that fits RJ10, unlike cat5 cable that goes with RJ45, is not usually organized in pairs. However, it is easy to mix RJ-anything cables with some existing cat5 infrastructure. So you must account for it. You don't explain what are the specific signals on your 4-wire connection, but if they are single-ended signals, there may be more crosstalk between them if you send two of your signals to the two wires of the same pair, rather than to two wires of two different pairs (in case the cabling is partially made with cat5). And if your 4-wire connection contains a differential pair, you should assign the pins appropriately so it ends up on physical pairs on cat5 cables. In short: take in consideration the fact that, in some infrastructures, a pair is formed with the two inner wires (pin 2 and 3), and another pair is formed with the two outer wires (pin 1 and 4).
Once again, because your cabling could en up being mixed with some existing RJ infrastructure, you should take in consideration the voltage levels we can usually find in these infrastructures, in case a cabling error occurs. The most challenging one being the telephone voltage levels, than can hit ~90V when the phone rings. So if you really want to be safe, you should protect the circuit against these high voltage levels.