Stripping dry-film photoresist safely at home
OK I did some research and will answer my own question in case somebody else is looking for some solid data on the health risks.

For the concentrations of sodium hydroxide and potassium hydroxide typically used for photoresist stripping (0.5% - 1%), both substances are classed by the European Union not as "Eye/Skin Corrosive" but merely as "Eye/Skin Irritant":

Classification of Sodium Hydroxide, Classification of Potassium Hydroxide

That is not to say they are completely harmless but at least reasonably safe at these low concentrations.

As a side note: Oven cleaners may contain up to 5% sodium hydroxide. They work in a pinch for stripping. Though leaving them too long will dull the copper surface.