try getting a 130 axle wheel in a 126 spaced frame and see if you want to do that with every wheelchange/ puncture repair.
if its a 27" wheel and by 10 speed you mean 5 cogs on the back wheel 2 on the crank it may be a 120, then you are stuck. have to get the frame spread and re aligned.

if you are considering the latest stuff with 10 cogs on the back wheel alone ie a 20 speed if there are 2 in the front,
Buy an entire bike or pour way much cash into this project.

a 120 dropout frame is more suitable for a single speed or an internal gear hub conversion.,
126 was the era of 6 speed freewheels or compact 7, 130 was compelled to get #8 cog on the end of 7 speed spacing.