It does not have to be another OT, but heck I have seen DE, LB come in on certain situation around the goal line and be more effective than I have seen from Hanna. As I mentioned he has been with Dallas since 2012 season and did not play at all last season yet I saw no slowdown from the offense last year to make me think Hanna's job was secured. If he can go out and show he can produce as more than just a blocking TE then great. Again not against him I just expect more than I have seen from him. He is a good blocker just not irreplaceable
Hanna and Swaim provide similar results; however, otherwise the Cowboys have struggled to find TEs that could perform the precise functions that they want from the 2nd TE. Escobar couldn't do it. Dante Rosario couldn't do it. Andre Smith couldn't do it despite excellent physical ability. Even MartyB couldn't do what they wanted.
The reason you didn't see a drop-off without Hanna is because Swaim is a similar type blocker that really knows the intricacies of the scheme. Once he was injured they played less 2 TE sets and Escobar had finally learned the scheme and was able to perform some of the functions that Hanna/Swaim had done previously.
They promoted WR Vince Mayle from the practice squad after Swaim was injured. This was an attempt to partially fill that role because Mayle physically looked like a small TE and he was really strong as a blocker. Unfortunately the refs screwed him over more than once calling his pancake blocks penalties. Eventually they had some injuries on the OL and wanted to call up Cleary and they tried to move Mayle back to the PS but someone claimed him.
They did have a little more success with Jumbo Joe than previous attempts at OL playing TE but that was only for short yardage.
They had a TE in training camp, Austin Traylor, that was really good at one-on-one blocking, but he made many mistakes in the preseason games and that was just playing as an inline-TE which is less complicated that all of the move-TE functions that Hanna/Swaim can do.
Moving a DE or LB over there is definitely not going to give them the guy to precisely execute his job within the scheme which is what they value more than physically dominant blocking. They tried guys like Montrae Holland and Josh Brent at FB and that failed. It always seems great in theory, but more often than not it does not work. The best I've ever seen in that role was the DT at Alabama a few years ago Jesse Williams. He didn't just blindly plow into the defense like many Lineman that have been tried at short yardage FB, he knew the scheme really well and had enough agility to go laterally to pick up the correct defender to block. He had a knee problem right after being drafted that kept him from even doing much in the NFL.
Rico could be the answer to this issue, but they'll likely limit him this year to the more simple inline-TE function and have Hanna or Swaim do all of the move-TE functions.