I've never tried using the vellum paper, but I've heard the printer ink takes pretty close to forever to dry.
The blocks I've made I used the full sheet label paper..it's white and when the block is on, it kinda/sorta has a transparent look.
Also, I'm thinking if you used the vellum paper..the string of lights would show through.

Here is some of my blocks I made. I just made the Fathers Day block for My DH. The other 2 I had orders for. Please let me know what you think.

Those are awesome ....... very elegant. Now , is this vellum that you printed on ? Did you do it on your own printer ? I want to make some of these so bad ... but I'm at a dead end on how to make a translucent print . My printer isn't that good . Ha ! I don't even know where to find a good print . I'm a lost cause ~~ LOL

TMG..I don't know if Grannyicu used vellum or not (BTW Granny..those blocks are beautiful, but you if just have to have it transparent, you might could try tracing paper. At least the ink would dry pretty quick on that.

Do you plan on using the string lights or the nightlight type light? If you're going to use the string type, I can almost guarantee the jumbled up string of light will show through on anything transparent. I don't know about the nightlight kind..but I'm thinking it'd probably show through too.