I wouldn't worry too much about the legality of the question
Since any of the forbidden go fast modifications would be all on the fire control parts & not the receiver or bolt, the question seems legit to me.
I have this book.
It's from 1982, so it's a bit dated but quite good.
http://www.amazon.com/gp/product/091067647X/ref=olp_product_details?ie=UTF8
They do a chop down of a Winchester model 70 to create a short length action that wasn’t being produced commercially.
You have to modify action, bolt and firing pin.
I've also seen bolt actions cut down to take a pistol cartridge to create a DeLisle type carbine.
I've seen both modifications here in Canada & there is not really any restriction on that sort of thing.
No one's going to stop you from cutting your gun in half

The only relevant restriction I can think of is a magazine limited to 5 rounds in a rifle.
Because the book is old, the welding technology is dated
On the bolt and firing pin, they are under compressive stress, they use silver solder/brazing
No idea what temperature or alloy.
They cut in the middle and use water or heat control paste to keep heat away from the critical Hted lug areas.
It makes sense since most bolt handles are attached with silver brazing the same way.
On the Win 70 action the action itself is in tension, so the weld is much more important.
They assume assume 4130 or similar alloy & use that alloy rod with gas torch welding and the same water or paste to keep heat from the critical areas.
Not only strength, but you need to keep the alloy the same so bluing will match.
I can see that TIG would now make more sense than gas welding for the action.
I would want to use a GOOD pro welder service.
Pre and post weld heat would be important for avoiding a heat affected zone and brittleness
I would want to do much more research on that.
It's an interesting project, but not simple.
Mandrels, jigs, milling machines are used to keep everything straight.
Sometimes projects are done, just for the sake of the project.
This bolt action mod makes sense to me, an SKS? Not so much, but it's cheap so have at it.
It would also affect your gas op rod length too.
SKS's were made in different countries to a wide variety of standards.
East Germany vs China?
Mods to lower power cartridges are safe enough, to higher ones – not on your life.
I agree with other comments, there are specific SKS forums with experienced users that have done those exact mods.
Every thing depends on the alloy of steel used
I would start with that
Frank de Haas, Shortening the 1917 Enfield Action Rifle 121 , January-February 1989
I'd love to have that article if anyone has it.