Go to BlackOps3Root/usermaps/scripts/zm/ and open the mapname.gsc file.
Find this line: zm_usermap::main();
Add the following:
startingWeapon = "anyweapon"; weapon = getWeapon(startingWeapon); level.start_weapon = (weapon);
Replace anyweapon with a weapon of your choice (for example smg_standard).
Save the file and rebuild the mod, you'll have the new starting weapon.