Okay... Trapse is not a word according to Dictionary.com, and I couldn't figure out how to say that word to figure out a rhyme for it. Did you perhaps mean Trapeze?
If you did I shall rhyme it with:
ease
(I know that's a chicken way out but it's all I could come up with!)
Dictionary.com Unabridged (v 1.1)
traipse
–verb 1. to walk or go aimlessly or idly or without finding or reaching one's goal: We traipsed all over town looking for a copy of the book.
–verb
2. to walk over; tramp: to traipse the fields.
–noun
3. a tiring walk.