Ok, so, here's what I think about this matchup.
Vegeta's got such a massive AP advantage that he could genuinely flex his aura and Ichibē would die. On the other hand, he lacks the speed advantage he would have with speed unequal.
Plus, he might try to tank Ichibē's zanpakutō or his ink since he doesn't know what it does, and that would be game over for him. Shirafude Ichimonji GG.
Ichibē's got hax on his own. Ichimonji's ink shenanigans would **** Vegeta over if they landed. Plus him trying to tank his zanpakutō's strikes and all that.
Futen Taisatsuryō is not his first move, and, unironically, fortunately so. Thanks to the anime we know how long the chant to cast such a technique is. And on top of that, Vegeta would probably just see it as something ridiculous and blast Ichibē to smithereens.
The problem with Ichimonji's stuff is that it has to land, and while Vegeta doesn't know what that is nor what it does,we know he ain't the type to just stand there and wait for the enemy to strike or allow himself to be hit a la Goku.
Dude genuinely might either try to punch or straight up go for Ki nuking with blasts. Or even explosive waves if the situation requires them. And Ichibē getting hit by them would mean game over for the monk.
The latter could either go for ichimonji's ink right off the bat or do what he did with Yhwach and start off with the basics.
To me, this looks like the classic "who hits first" situation, 50/50 situation, whatever you wanna call it. so...
I vote Inconclusive.