Yes, they do make up 308 diameter bullets as light as 95 grains. Maybe even lighter.
If you want to use the 7.62x39 for varminting, you should make up a varmint rifle chambered for it, with a .308 match grade barrel, with a 1-15 in twist rate.
Keep the chamber tolerances as close as possible, to match grade standards and of course have a short throat.
The Spanish, made up 30 cal bullets for their CETME rifle/cartridge combo that weighed 112 grains. They had a lead base and a plastic nose insert, all surrounded by a fmj.
I was lucky enough to pick up some of those bullets from SFRC. They shoot very well in my 308 barrels that have a 1-12 or faster twist rate. This is because they were designed to be the same length as the 7.62x51, 15 grain Nato cartridge and so that they could use international Nato ammo in their rifles.
These bullets are extremely accurate in good rifles, with good bores. Match quality is a very close description of their performance and because they are so light, they can be loaded to very fast velocities.
Now, OP, the bullets you describe, are usually made for the M1 Carbine or pistols. They don't have the strength or shape to be very fast or very accurate out of normal chambers.
They do make some very decent 125 grain bullets though that would be good for varmint hunting and are constructed strong enough to get some very fast velocities out of. These can be seated out far enough in a standard 7.62x39 chamber to give good accuracy.
If you're planning on using an SKS as a varmint rifle, IMHO, don't bother. You will be disappointed and likely wound a lot of game.
In the end, it would be cheaper to pick up a used 223 Remington and go from there.
That being said, I made up a rifle for a friend recently. I had an M96 Swede action and a spare bble in the box and decided to put it together to see how well it would shoot the Hornady V Max 95 grain offerings. It did really well. Even with that long military throat, designed for 160 gr round nose bullets, it shot into less than an inch at 100 yards, with a 35 year old Redfield 3x9 Widefield, range finding scope.
My friend is tickled pink. It shoots as well as his 25-06 and is lighter in weight as well as recoil.