I was going to replace my neutral safety switch when all 3 bolts broke off.

This is in fact an automatic transmission? If it is then this is called the park neutral position (PNP) switch. Take a look at the adjustment procedure below and make sure that is the part that you were replacing just so we are talking about the same thing.

If it is, you can try self tappers but if it were me, I would grind them flat, center punch the old bolt and then drill and tap a new hole with new bolts. Here is a video that will help with this if you need it:

https://www.youtube.com/watch?v=YDt5OUIZTs0

The issue with using self tapping screws is they could crack the case then we are in trouble, second once you remove them, they don't seem to ever tighten as well. Lastly, this position switch needs to remain solidly in place or the switch will possibly come out of adjustment and you will have to go through this adjustment process over and over.

Let us know if you have other questions. Thanks

Very good point and I did not think of that. In that case, you may not have another option unless you remove the transmission or enough out of the way (if possible) to get enough room.

I am sure you will be fine for a while if you use self tapping screws. You would just need to keep it in mind that if it loosens it would cause an issue with the alignment/adjustment.