you can replace just the axle, just remove your axle and take it to any bike shop as long as it is not a sealed bearing axle any quality shop should stock basic loose ball axles. swap over the cones and spacers and your golden.
it does not matter if it is a bmx, fg, road, cruiser they all use 3/8" and similar sizes axles just the length will vary.
if it is a sealed bearing hub the just google fourmula replacement axles and you'll get several hits.