Call his bluff? - so you mean you have already made up your mind he is cheating on you with this woman?
tell him I messaged her - are you actually going to message her? Only do that if you want to look like a jealous bunny boiler. Or do you mean, pretend to him that you have messaged her? Only do that if you actually ARE a bunny boiler.
Stop playing games, stop interrogating him, & stop texting him about your insecurity. It's not attractive behaviour, & will not make any difference at all to the facts, which are:
He is either telling the truth, or he is lying.
You either trust him, or you do not.
If you continue to cross-examine him about this woman, he will dump you.
This is a hell of a lot of drama for a new relationship.
Also, each of you are recently out of other relationships. You must still be in the 'rebound' stage, because your suspicion & paranoia about some random woman snapchatting him even though he has turned her down is obviously stemming from the insecurity your previous man's sleazy behaviour instilled in you.
Why not work on that, through therapy, or reading up on self-esteem, instead of projecting it onto your new man?
What's the worst that can happen?
You decide to trust him, enjoy his company, & sure - you could get blindsided with a later discovery that yes, he is a cheat. And that will hurt you. But you could say that about anyone you get into a relationship with - any human has the capacity to cheat. So the only cure for your insecurity is either to never date again - or to get to the root cause of it through therapy & self-development.
Hope this is all a storm in a teacup OP.
Stop stirring the pot now, & focus on what YOU enjoy about your b/f, & forget about Ms Initials On My Facebook. She's not the problem - your relationship-destroying insecurity is the problem.