I know that seedless watermelon seeds are the result of a hybridization. So, you have to buy new seeds each year. Maybe seedless cukes are the same.

great for the company, rather sucks for us.

I think seedless cukes are bred so that they produce fruit without the need for fertilization. Even if there are seeds present, they're probably not fertile. The fact that they're paper thin suggests that they're not, although you get the same thing if you don't let the cuke ripen to way beyond eating stage, which is what you need to do if you want ripe cuke seeds.
There are several cuke varieties around now that do this. Such varieties are called parthenocarpic, I think.