97 is a Mercury lower unit. If it is a 4 1/4 diameter lower, the prop will fit. If it is 4 1/2 the prop will not.
Either measure the inside flange on the prop hub or ask the owner to do it if it is an auction. It should be less than 4 inches. Any more and it will not plug into your 88 lower unit.
According to my prop book, the part numbers are different so I would hazzard a guess that they will not swap.
Clarify please. Do you mean the prop shaft is sticking out of the prop by about 1/4 inch and the nut will not tighten the prop? If so, there is a spacer that fits under the prop nut for that.