You'd be okay just making a simple contract, basically so long as you have something in writing and both parties agree to it you should be okay and not need to worry.
Here are some things to read that should give you a pretty good idea of how to set up a simple contract geared towards music/audio:
https://www.gamasutra.com/view/feature/132537/game_audio_contracts.php -contract structure and pointers
https://vi-control.net/community/threads/how-do-you-make-a-contract-for-music-in-video-games.90291/ -Discussion and pointers
https://www.reddit.com/r/WeAreTheMusicMakers/comments/2r4x1t/signing_my_first_contract_as_a_composer_for_a/ Basically the same as the last two.
Hope this helped!
