Leave them as they are.
Even if the solder could be removed, the pressure of the bezel on the periphery of the coin leaves permanent marks that could not be corrected.
You will have a much easier time selling these if they remain in the bezels, as they are.
As to value, just going by gold value only for the coins themselves, the $10 has $528 and the $5 has $264 worth of gold. That's for today's values, which will fluctuate.
The bezels themselves also contain some gold, although if they were separated they would be scrap gold only. Which is the main reason to leave them alone.
If you were to buy a new bezel for the $10 and $5, it is likely that you would spend well over $100 for ones like you picture.
However, the coins still retain some numismatic value over simple melt gold value. How much depends on where you would sell it.
Sold on
ebay, you would probably get LESS than gold value after you paid
ebay fees, Pay Pal fees, and postage.
Sold to a jewelry store, you might get a little better than gold only.
Sold to a coin shop or dealer would probably get you a few more dollars, but not many more.
Sold to someone who wants the for presents, maybe even a few dollars above that.