Beware, these urethane bumpers
can be repaired. There is a good article by Lars Grimsrud on this subject that can be found at corvettefaq.com (let me know if you don't find it, I propably have it on my computer somewhere). I did not succeed very well to repair mine, but on the other hand I didn't use the right materials. (I tried to repair it with fibreglass on the back side, but it will not bond very well to the urethane)
The hardest part? Well try lying flat on the floor with the arms raised straight up towards the ceiling for one or two hours, and you will get the picture...
Well seriously, if you are sure that you will never use the old bumper than you might aswell cut it. You should not use the old fasteners again, there are a new type of fasteners that can be bought from most major vendors, and these are much better to use than the old type.
The new bumper is not exactly "bolt on". You will have to drill holes for the fasteners, the "corvette" letters, and also make bigger holes for the license plate lights, and some other tweaking around the tail lights. A dremel will come in handy.
Word of advise regarding the fastening holes; there are small "dents" in the new bumper where the holes are supposed to be. These migh not correspond with the holes on your car! Put the bumper on the car with duct tape or similar, and try to mark from the "backside" with a pen or a sharp object where the holes are supposed to be. Then make these holes "oval", so that you can adjust the bumper before you tighten the bolts.
Then there is the issue with the fit to the car. When I first tried mine on my car, I thought "no way this will fit". The car was almost an inch wider than the bumper. But they can be bent pretty much. Try to fasten the bumper with the upper middle bolts first, and then you can fasten one bolt "outwards" at the time, while you try to bend it in place. A friend with an extra set of hands might be useful here.
I have some photos that I took of mine before and during installation. The idea was to make a guide for this and other projects, but I never seems to find the time.
http://hem.passagen.se/corvette74/bumper/