First, I don't understand the need for a cath AND a TEE. It seems like overkill.
But, as far as the cath, you can usually choose how "with it" you want to be during the procedure. I chose to be darn near fully awake, because I wanted to see everything. However, they are perfectly willing to bring you to "nearly out," as well.
Having seen it once, I found it less than enthralling, so I will probably let them zonk me out for the next one. Even in my awake state, there was no pain while the catheter was in use. There was only the bee sting of the local painkiller shot. You can feel the thing poking into your heart if you're on low meds, but it doesn't hurt. It's just vaguely disconcerting.
I did experience some angst as they held the wound closed at the end. Apparently, I have an unusual amount of nerves there, and it amounted to having someone put pressure on your funny bone. I gather that's not too common, though.
There are even folks on this site who have no problem doing a cath without any meds at all.
Best wishes,