Cutting plastic stocks is VERY "iffy", and mounting a sling swivel difficult due to the hollow stock, and the lack of a good anchor point for the swivel.
The hollow stock makes re-drilling holes for the butt pad screws chancy since there may not be enough material left to hold the screws.
Since the factory swivel is actually molded in place it holds.
The stock is really too thin to hold a standard stud, so the only thing you can do is use a stud which has an internal nut to hold it.
What I'd recommend is just buying a short stock, and selling the one you have to help fund the new one.
Special shorter stocks are sold by Speedfeed, (who makes Remington's synthetic stocks) by Hogue, and several others.
These are sold as "youth" stocks and as Tactical stocks for use with body armor.
In either case, they're just standard stocks with a shorter pull.
NOTE: Speedfeed is a BRAND name. The make many stocks, SOME of which have an internal magazine for extra shells. Not all of them do.
The Hogue Over-molded stocks:
http://www.getgrip.com/main/overview/shotgun.html
The Speedfeed/Remington stocks:
http://www.speedfeedinc.com/