How do I differentiate between different types of installed wire lock/safety wire on planes?
Monel is more expensive than stainless steel so it's use is limited to where it is an advantage, mainly in high temperature applications such as securing engine accessories, piping etc.  If the locking application is not in a high temperature, high humidity, high oxidisation area, then it's probably stainless steel.

There are chemical tests you can do on small samples using acids and reagents but you asked about an installed lock. The only way I know for testing an installed lock is to  polish it. Monel is duller than stainless steel and does not polish to a shine so  the quick way to tell is to try to polish a piece of it with a cloth.  If it shines up, it's stainless steel.  If it doesn't, it's monel.