FMJ is fine if it is lead core. I am assuming that your 7.62x39 is STEEL core... which is what makes it a no no at most indoor ranges. The reason for this is that the steel projectile damages the backstop. At outdoor ranges the backstop is usually just dirt, so steel core is fine.
so to answer your question, there should be no issues with your ammo at an outdoor range.
But check with your indoor range as well, as some of them do allow it. Just ask before you go!