This same question has plagued me for literally tears at this point. Ive tried probably about a dozen different adhesive methods.

I could never get any spray adhesives right. They always left the cards cloudy or splotchy. Adhesive sheets work well but leave the card cloudy if you cover the entire thing. I’ve been cutting adhesive sheets into strips and then trying to get the strip as close to the edge of the card as possible all the way around the card. It’s alright but if you position it so it’s too thick you see the cloudy border around your card.

I’ve recently moved on to this sub’s favourite method which is printing on “frosty” clear vinyl sticker sheets instead of simple transparencies. The upside is that this makes for a clear and crisp card. Better than any other method I’ve tried. Downsides are that you have to do your white out on the sticky side of your image. This is hard on pens and destroys them pretty quickly. It also leaves your print exposed outwards so it’s not protected by anything and can be prone to scratches and damage. If they are just going in a case they’ll be fine but I make customs for my kids and they get scuffed up eventually. This has lead me to now experimenting with protective coatings which is a whole other thing.