Taking a look at their web site, it appears that "Wedi board" is, effectively, a foam version of drywall appropriate for both wet & dry locations. (I looked it up because I had no clue what it was. I included the info here because I figure others in the US may not know either.)
Their web site shows the washers installed with a Phillips head screw through the center hole which appears to be recessed slightly from the surface.
A pan-head screw would work nicely because it's got a flat bottom to hold nicely in the flat of the washer's recess, however the domed top may stick up above the recess and create a bump in the finished surface. At a minimum, your tile mastic (making assumptions...) would have to be thick enough to cover the screw head. If you can find a pan-head with a shallow dome available with a waterproofing treatment, that may be the way to go.
A typical wood screw has a sloped shoulder that will crush into the washer's recess a little bit, but has a flat top that you should be able to get flush with the surface of the washer.
I would think that pretty much any wood screw would work in that situation.
- You could use a drywall screw, as those hold drywall up very well when screwed into studs. However, they're not really designed for wet locations and you may end up with corrosion and screws failing due to humidity and leaks.
- You could use a galvanized decking screw, since they're designed for holding in wood and are good for wet locations.
- You could use a screw designed for cement board, as these are similar to drywall screws, but are protected for use in wet locations.
- You could contact the manufacturer to ask what they recommend, then post that here as an answer to help others out.