Would the replacement cap need to be 250V Ac? I can find various ones at
250 VDC, 250V AC seems to equate to 630V DC in the specs.

Would an electrolytic capacitor be correct? How does that work with
polarity (seeings its getting AC)?

Cheers

No, you'll want a mylar or other similar capacitor, at least 250vac rated,
but personally I'd look for something with a 400vac rating. If you can't
find one I probably have one in my junk stash I could send you for the cost
of postage.