OOC
Sorry, Anora, I read your question and meant to respond, but then totally forgot about it...
You do have proficiency with the vibrostiletto; it is a martial weapon with the Finesse property. You would roll +4 to hit and 1d4+2 for damage. Also, it scores a critical hit on a 19 or a 20.
Yes, you can do that. Your attack with the blaster in your right hand would have Disadvantage due to the creature being in melee with you. And your attack with the stiletto in your left hand would only do 1d4 damage, but it wouldn't have Disadvantage.