The S-10 can probably do it, but you will be at or near its upper limit.
I hauled a 1965
Safari from Georgia to Utah a year ago with a V8 Explorer
and to honest I was glad I had the extra towing capacity of the V8.
If you chose to do it, overlander64's suggestions are good, I would add:
Have the trailer bearings and trailer brakes (including all the brake wiring)
checked, since your S-10 isn't overkill you need to know the trailer brakes
are defiantly going to work.
I would plan the trip home so that you:
1) don't have to drive through any major cities during
morning or afternoon rush-hour.
2) I'd plan on only 55 to 60 mph.
3) I would avoid driving at night, unless you are real comfortable doing that.
There are two sides to this issue; there will be less traffic, but a higher
percentage of the traffic will be BIG TRUCKS going faster than you
(those guys will give you a wind blast that you will feel).
4) If you detect any engine pinging while pulling up hills up-grade to higher
octane gas. I would do this before you cross the sierra anyway.
There will always be those that will tell you to never do this or that.
I would say, know the limitations, respect them, plan appropriately,
and don't add any extra issues that can be avoided by careful planning.