How do I move a door hinge out 1/8" (door is too tight to the stop molding, makes "paint popping" noise)?
In almost all cases its better to move or adjust the strike plate, the stop, or both rather than move the hinges. Here's a series of diagrams that demonstrate why (dimensions are exaggerated for effect) :


This is an ideal door set up. The gap between the door and the stop is an even 1/32 to 1/16 all the way around. It is not supposed to be tight to the stop. I use a credit card to space my stop off the door when setting a new door. Note that the door is held in its position relative to the stop on the swing side by the opening of the strike plate. In newer strike plates there is a tab inside the opening that can be adjusted without moving the plate itself but older hardware typically does not have this feature.

This shows how if you only move the hinges as you're suggesting, it will not fix the problem on the swing side if the stop and/or strike are not moved as well. 

This shows moving the strike but not the hinges. It will only open the hinge side reveal a small amount but that may be all you need. The down side is, as you can see, you can only move the strike plate a small amount (which is all it takes in most cases) before it brings the face of the door out alignment.

This shows moving the stop which solves the problem without having to move either the strike plate or the hinges but it will require you to disturb the paint. I understand your reticence in tackling lead paint mitigation but it's not insurmountable. Here is a thorough homeowners guide to properly handling lead base paint posted by the state of New York's health department. Take the precautions specified, and you should be able to safely relocate the stop and get the results you're after without too much risk.
If you do absolutely need to move the hinges, follow the instructions Diceless posted, they're right on. I'll only add that you might want to place a shim the width you're trying to offset the door in the back of the hinge mortise to keep the hinge from settling back into its original position before resetting your doors and to fill the void that will be left behind.