Teeth trimming is not the same as cutting them to the point where they cannot damage a snake. You'd need to cut to the gums and after a quick search, they DO have a nerve in their incisors that you would have to cut to do what you want. (Source, ratbehavior.org/teeth.htm - anatomy of a tooth section)
Definitely do not torture live rats like that just to feed a snake.
Either accept the risks that might happen when feeding live if it becomes necessary, learn all the methods to avoid live feedings with a potentially finicky snake, or choose a snake known for take frozen thaw easily. (Including most colubrids, carpet pythons, boas, etc.)
I have a few snakes who do better with live, and it is my personal choice to feed this way to those snakes. I take full responsibility if something happens. To that end, I breed my own rats from exceedingly good pet quality lines and even after being struck, none of my pups or older rats have even attempted to bite down on the snake reflexively despite the pain (pet store rats fed a few times previously all attempted to bite ones they had been grabbed by the snake).
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