I work often with TSDoctor and I cut ts-files with that, too. There are no freezes or stuttering. But TSDoc cuts the movies only at I-Frames. The cutting is not frame exact.
Yes an export without menu is possible. BUT the most DVBTV-transport-streams are not compatible to the BluRay standard. In this case TAW will reencode the movie.
For your case try: VideoReDo, TSDoctor or TMPGEnc MPEG Smart Renderer 5
http://tmpgenc.pegasys-inc.com/en/product/tmsr5.html