Without modifying the action itself, you're looking at the same size as the factory bolt body you currently run or not much bigger. I know there are a couple of companies out there that make aftermarket bolt bodies, perhaps a call to one or any of them would help?!?
Sharp Shooter Supply comes to mind first off, but haven't heard good things about being able to get a hold of them very easily.
PTG makes replacement bolt bodies that you can order from Midway and probably a couple of other vendors as well.
PTG Bolt Body Savage 10 Short Action Spiral Fluted
The link above is a spiral fluted bolt body for a short action Savage, that states it is a better fit than a factory and may clean up any play that your current factory bolt body displays.
Hope I helped and good shooting!