It's not really that big of a deal, it is messy though. You don't want that to get anywhere you aren't wanting stripped.I'm going to have to do this myself so media blasting is probably not practical. I've heard that one of the biggest problems with using chemical strippers is neutralizing and removing the stripper.
All that said, some 80 grit and then 180 grit and a DA is probably the safest way to go.