Exhaust sizing questions for catalytic converter

I am currently redoing a lot of stuff on my Integra with regards to the motor. With the amount of oil consumption it had I am thinking it is good idea to just replace the current highflow catalytic converter on it.  But I do have some questions with regards to exhaust flow and exhaust sizing and specific issues I might encounter with the plans I am doing with regards to mating it up to my catback exhaust. Using some illegal adjustable testpipes (lol), I am looking at adding cat to them because they have the needed flanges and piping. 

On the header end I have a JDM Iintegra Type R 4-1 header that has a 2.5in collector. I had a friend weld a 2.5in flange to the cat so I could connect it to the header, no problems there and what I plan on doing again with the new cat. 

The next part is where I have some questions. Following what I believe the JDM Type R had, the catalytic converter rear piping goes down from 2.5 to 2.25 in piping, I replicated this setup on the cat so I could bolt it up to the stock exhaust, but when I took off the cat to look at it, it comes out I actually bought a 2.5in exhaust flange and it was welded to the 2.25 in piping without issue as pictured below:

I did not realize a 2.5in flange would bolt up to the 2.25in flange so it got me thinking to just have it welded up without any reducer like last time. Test fitting the test pipes with the cat I bought, it looks like I have a setup that would require no cutting and about the same length as my current cat once it is welded up.

My question is, how bad of an idea is this if I don't have the reducer of 2.5 to 2.25in into my current exhaust? The cat will be at 2.5 from the header flange and at the rear instead of 2.25. Is exhaust flow going to be that much worse with that kind of bottleneck? or is it going to minscule that it I'll just lose a few HP? Without the reducer, it sounds like a stepped bottle knock vs a smooth flowing one might be worse? if I am looking at it visually? 

I know I am already losing power going down to the smallish stock ITR exhaust, but it sounds great and isn't loud on the street. But at the same time, staying with 2.5 all around would allow me to consider future upgrades without modifying the cat.

My gut is telling me that for street use you will not notice the difference.   It got me thinking. We use to put 2.25 inch duel exhaust systems on sb 350 cid (5.7l). So in theory 2.25 is ok for 2.85l motor.  If this was a track day toy that was going to only live in the upper part of the rpm range then yes a strait 2.5 system may be better but then headers and other things become important as well. Also if it was a track only car we would probably not be talking about putting a cat back in it.  
 

So in short I think you will be fine. It may make it a bit better as a street car. 

dean1484 said:

My gut is telling me that for street use you will not notice the difference.   It got me thinking. We use to put 2.25 inch duel exhaust systems on sb 350 cid (5.7l). So in theory 2.25 is ok for 2.85l motor.  If this was a track day toy that was going to only live in the upper part of the rpm range then yes a strait 2.5 system may be better but then headers and other things become important as well. Also if it was a track only car we would probably not be talking about putting a cat back in it.  
 

So in short I think you will be fine. It may make it a bit better as a street car. 

Thanks that was also my line of reasoning especially with a street car being a compromise of everything.