I have done a few and they are all different. So far I have chopped a Win 70, Steven 200 and a Baikal MP-153 synthetic.
For me the swivel studs were not an issue, but if they are I guess, some filling of the hole and moving the studs might be in order.
For the Win 70, I simply chopped an 1 1/2" off the stock and installed a new pad, very simple.
For the Stevens and the Baikal, I chopped the stock and then had to install a small block of wood roughly the size of the inside of the stock (3/4" ply wood for one and 3/4" spruce for the other) This was epoxied in place, be sure to use a good epoxy that will stick to the plastic and scuff up the plastic inside. This was necessary to install the pad as the screws did not line up.
In this case the block of wood only roughly fit tthe stock, so a good sandable/drillable epoxy was used to fill the gaps. If I was doing this again, I would likely inset the wood by an 1/16" or so an then fill with epoxy to make flush with the stock.
With the Baikal I had to also bore a hole to access the receiver screw and with the stevens, I had actually installed 2 blocks of wood and sandwiched a recoil reducer in there, I also drilled a small hole in the stock and filled it with spray foam to take out the hollow sound.
For your swivel stud, you could use a dremel, knife etc and remove the plastic where the stud screws in and then epoxy a block of wood there as well (hardwood would be best). But by installing the block fo rthe pad, you can now make new holes for your pad and they may noy interfere with your studs. If you have to do any cosmetic work to the outside of your stock, you can easily repaint it with Krylon fusion it will not scrape off if you follow the directions.