That's the challenge when dealing with stock sized gear.... the chest might fit but then the other stuff is all out of whack.
I lift in an Overkill shirt. All overkill gear is made to your measurements so it's dead on. The first workout took a hand full of baby powder, a ratchet tie down ( overkill puts pull tabs in their shirts for these) and two guys to help me get in to it and it still took a good 5 minutes... The first few sets it was so tight that I needed a spotter to get my hands out to the rings on the bar. By the second workout it was easier to get in to, I could get my hands to the rings myself and I could touch a 2-board. By the 3rd workout it took 2 minutes with the ratchet and it was on and I could touch weights with it.... and it's stayed pretty much the same since.
That's how you'd want a shirt to fit ideally for an experienced lifter.
Now, the Katana is a tough shirt to touch in ( about as hard as my Overkill) and it sounds like you are pretty new to this.... if you don't have an experienced crew to help you then don't sweat it. Start there and after a few workouts take it to a tailor or shoe repair shop and have them tighten the arms 3/4". Don't try to do it yourself and don't use regular cotton thread. The gear companies all use a #41, #69, or in some cases a #81 nylon bonded thread. I do a lot of alterations for my gear and for my buddies so I just bought an industrial sewing machine and do it all myself. I use #69 thread and I have never had a blow-out. Either way, start out loose and as you learn it, tighten it up.
If you have a crew that knows how to work gear ship that thing back and get a size smaller. You shouldn't get anywhere near doing a pushup in a shirt unless you have 12" long arms and an 11" gut. Even a single-ply katana shouldn't come close to this. And if you are pulling your arms back on your own then it's definitely too loose. The first two or three workouts in a properly fitted shirt should involve 10 minutes of sweating and swearing in to your shirt as your whole crew tries to stuff you in to it.....
The big one, and I know that this isn't your question.... if you don't have a crew helping you that knows their shit bench in a cage and set the safety catch ( or tow straps hung from the top bar) to catch the weight before it smashes your face. Benching raw if you miss a weight it's slow and predictable, a shirt adds a whole new dimension of cluster-fuck. If something goes wrong it happens much faster and you need good spotters ( or a cage so you at least don't smash your face).... usually it's one of 2 things. Some guys will dump the bar on their bellies when they try to touch ( especially new guys who can't handle the pressure of a shirt and panic), or 2- the bar pops up so fast from your chest/belly that you don't get your elbows out in time ( or your triceps give out) and the bar comes back over your face and either the spotters catch it or you lose teeth... as in all of them.
So be careful, use safety pins, or make the field trip to get some work in with a good team. Either way, good luck.