Homemade kimchi cucumbers aren't crunchy
one of two explainations:
They are over ripe, it goes mushy if you keep them too long or (more likely reason) you did not salt properly. When you salt it does go a little limp but it retains crunch for a long time (think pickles).
I also tend to stay away from most cuke varieties except kirby (which is widely available) and korean (which as you guessed the best for this). I have used english hot house cukes and japanese but it doesn't come out as cruchy or good.