Hi H2,
The answer is no. You can't customise prompt dialog as it's the standard javascript function.
If you want to do it, I recommend you to create a "fake" dialog html window, with everything set up as you wish (input width and without Cancel button). Then you'll have to pass the value entered to a parent window, search this forum for an answer how to do it.
But I'm sure that you won't be able to avoid visitor skipping the form. Even if it will not have any Cancel button, anyone can close it using common [x] button at the upper right corner that is on any window.
good luck