Go for it. I'd get a 7 or 8-speed cassette so you can use your original shifters, they should still index fine. 9 and 10 speed cassettes have too narrow of spacing. Do you have downtube shifters? If so, they might be able to go beyond the last indexing point, allowing you to run an 8-speed cassette with the last two shifts being friction. You can test this by disengaging your shift cable. Pull the shifter back through all the indexing points, then try and pull it further. It should just slide back like it's in friction mode.

You can also get new shifters if you want. That will allow you to run however many speeds you want. 10-speed downtube or bar-end shifters are out there. You can probably keep your rear derailer unless it's worn out (or happens to be Dura-Ace!)

Regarding the spacing, you can jam it in there if you have a steel frame. But what I did when I put my 130mm wheel in my 126mm frame was just to remove the washer between the left locknut and cone. This reduced the spacing about 2-3mm allowing the wheel to slide in without stretching my frame. It was such a small difference I didn't even have to re-dish my wheel.