With the axle removed, it is not uncommon for the center spacer to be loose between the bearings. Especially if the bearings are worn.
The proper way to repair it would be to remove the old bearings and seals and clean all of the dirt and rust out of the spacer and hub and replace the bearings and seals with new ones. Be sure to pack the new bearings with grease and heat the hub to remove the old bearings and to install the new bearings.
You could probably get away with just installing a new axle and if the wheel doesn't bind when you tighten the axle, the spacing should be ok. But, for the price of new bearings and seals, just do it right and you won't have to worry about your wheel coming apart. :cool: