Depending on the cat that is on there, there could be gains made w/a high flow cat.
Yes, leave the muffler out. It will be comparable to a non=cat car that has glass packs on it. I had a station wagon and w/its long exhaust pipe, my wife didn't even notice. Back before cat=backs were common, this was a more common mod. It is a cheap alternative to spending big-bucks for and exhaust system that will mostly just sound cool (yes, it will probably accelerate better than stock, but how will it run at 3,500 rpm on the freeway).
Back pressure is not needed, in fact it works against you. Exhaust pipe works like a garden hose when it is being used to drain a water-bed. The column of gas has a scavenging affect in that the gas' high velocity, from the cylinders that fired a few sparks ago, sucks out the exhaust gas from the cylinder whose exhaust valve just opened. Then, the velocity of the "air" in the exhaust column starts pulling the air in, through the intake valve, before the piston starts going down and sucking in the air. Most people say back-pressure, but you need exhaust gas velocity, that comes from smaller pipes (as a side-point, on a 350 Chevy, generally speaking, for an all around motor, you want long smaller tubes on headers, for an rpm motor, you want bigger shorter tubes on the primaries, and for a dragster, you want short fat exhaust, all of them have high exhaust velocity at their target rpm). This brings up something quite important...in order for your motor to run "Right" all of your mods have to work together. If your exhaust doesn't match your intake it won't run up to its potential.
Just wondering, if you go to a cat-back exhaust system w/a larger pipe, what is it gonna do to your back-pressure? Most people don't know how fast their car is and they don't know what sort of gas mileage that it gets (All that they know is that they can drive to work all week long on a tank of gas).
Also, pipe diameter affects noise. I once put a 2" exhaust from the muffler back, on my Astro van, and my wife complained.
It is gonna be loader, but how much? My guess is that it will be like my '80 Toy 4x4...When I got it, it had headers and a glass pack and then the exhaust turned down to the ground, right under the cab. Now that was loud!!! I added exhaust all the way out the back, and it was considerably toned down and was just about right. Get you a saw's all ($20 at Harbor Fright), then cut off the muffler, or drop the exhaust and use a hack-saw. Run it and see what it is like. Try it out, keeping in mind that if the sound is taken all the way out the back, it will be quieter. If it is to loud, then get a resonator and add it to the end of the tail-pipe. BTW, all this is based on you having access to a welder, or a friend that welds....although any muffler shop would be happy to do the mods for you....you just don't want to have them weld on a pipe, and then pay them to cut it off in order to weld in a resonator. You may be able to use clamps...I like to weld my stuff in place. But, clamps work just fine.
Based on the picture, this has a resonator, in the center, just like stock, and another resonator at the end. You might also try a turbo muffler in place of the stock muffler. The big question...how load is it gonna be.
http://www.yonaka.com/Yonaka_1996_2001_Honda_CR_V_Catback_Exhaust_p/ymcb-crv9601.htm