Is it safe to import my private key into another wallet? I sent some bitcoin to my bitcoin core wallet before it synced, not knowing this sync would take days, and was wondering if i was to import my private key into a different wallet if that would work?
It's safe as long as you're sure that no one else has access to that private key. 

For example, you shouldn't import a private key someone else gave you. They could send coins to that key to make it look like they sent you money, and then steal them (since they have the key as well). 

If it's just copying one private key on one of your own wallets to another one of your own wallets (both of which only you have access to), then you should be fine. Just be aware that coins given to that key will appear simultaneously in both wallets, and coins spent from that key will disappear simultaneously in both wallets as well. This doesn't sound like an issue in your case, since you won't be using the old one at all. 

The alternative is to just do a standard bitcoin transaction to transfer it from one of your wallets to another. Although, I see that this is made difficult by the fact that your Bitcoin Core client not fully synced with the network.

Related: Did I just create counterfeit bitcoins?