Not wearing a regulation space suit, because it would exclude all the relevant radiation. Nor if you took it off, because you would be dead before the ultraviolet could do much obvious harm.

But if you got someone to make you an ultraviolet-transparent suit (which is a hard thing to do) then you would burn very rapidly very badly, and pretty quickly fatally. UVA is what gives you a nice tan on Earth, but most of it gets absorbed by the atmosphere. Above the atmosphere it would be several times more intense than your skin could take for long.  Only a little UVB gets through the atmosphere, but that little lick  is enough to cause most sunburn.  There is enough of it up beyond the ozone layer to take your skin off pretty quickly.

Practically all our UVC is absorbed by the atmosphere. The only UVC down here is from nuclear weapons, germicidal lamps, electric arcs and so on. What it would do to you up there you don't want to find out.

Even if finding out would asphyxiate you before you noticed the UV at all.

Cheers,

Jon