First thing I'd suggest is find out if your axle housing/4 bar brackets are really off by a 1/4", or if the setup is wrong. If the brackets are symetrical then the adjustments are off by 1/4". Make that right before trying to do different wheels on each side to cover it up.

As for your basic question, yes, the housing has to come out so they can get a good square cut on the axle tubes and then a good weld all around when reattaching. If you have someone who knows what they're doing perform the operation they'll jig the housing up with a long rod and centering blocks in the bearing points to maintain straightness during welding. Cost varies from area to area but you can probably figure around $500, or more if you have someone do all the work involved of taking out the axle, reinstalling, etc. If clearing the caliper is the main issue, and you've already prepped your mind to change wheels why not go up one size in diameter, e.g. 15 to 16". A new pair of tires would be cheaper than narrowing the axle.