I'd go with new wire. The problems with connections, even soldered ones, are more of a headache than it's worth, I think. Since you're only extending the wires by a foot or so, I don't think you'd need to go 4ga., but it wouldn't hurt.
instead of cutting them why not just add an extension with a m/f bullet connector so it could go back to stock if need be?
Bullet connectors on battery cables is a bad idea. You need all the juice you can get when starting, and terminals create resistance. Also, I don't think it would be economically viable to buy bullet connectors for a battery cable, if they're even made. The closest I can think of would be welding cable connectors.
It would be just as easy to make new cables and hang on to the old ones. I had a local battery shop make some for me- told the guy the length and gauge I needed, and he made them in less than 15 minutes, less than $20 for wire, terminals, heat-shrinked and color-coded.