I have worked with and installed everything from laminate to granite, including all solid surface products.
Due to the type of material swanstone is made of, I believe you will have a hard time getting any coatings to stick to the surface.
If you decide to try the re-finish of the surface, sand the surface with either 180 grit sandpaper or 40 micron sandpaper.
Once the surface is completely sanded, clean the surface with denatured alcohol until there is no dust or anything to hinder the purchase of the product you decide to use.
If the product you decide to use is an epoxy based product you should have a good chance the product will adhere to the surface.
I would try to tape off the sink.
To make the sink look better, remove all the plumbing fixtures of the sink, sand the entire sink starting with 150 grit sandpaper, then, sand the entire sink with 180 grit sandpaper and clean the sink of all dust with denatured alcohol
To finish the sink, sand the sink with a PURPLE scotchbrite pad and that should return the sink to original finish.
Good luck on your project and let me know if there is anything else I can do for you.
If worse comes to worse, use a green scotchbrite pad if you can't find any purple pads. JW