You can use any type of lock anywhere in or on luggage. The TSA approved ones just make it easier for them to inspect. Any other type would be cut or broken. and from then on, the container would be unlocked. I use tie-wraps of different colors.
Using a Different Lock
Federal regulations do not require air travelers to use TSA-accepted luggage locks or remove other types of locks, however passengers using non-TSA-accepted locks do so at their own risk. Should a bag require additional screening, TSA officers have the right to remove the lock to access the contents. Locks that do not open with TSA master keys may be cut from the bag, which may damage the suitcase in addition to destroying the lock. In lieu of a TSA-accepted lock, use plastic cables or zip ties; these can be removed easily by TSA and are inexpensive to replace.