Are your shifters indexed, or friction? Pretty sure the 7 and 8 speed cassettes would be compatible if you use friction (might have to adjust the stop screws on your RD). If you have indexed - either you need to switch to friction mode, get 8 speed shifters, or live with the new 7 speed cassette, or use the new 7 and get a chainring with a tooth or two more on it.
edit - why not remove the lockrings and move good cogs from the new one to the old one?
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Last edited by USAZorro; 05-18-16 at 08:59 AM.