Say I ulted someone as Shen and for whatever reason needed to not teleport (only want the shield for a teamfight where I'm already there, if ult into a fight where I know I'll die, etc) Is there a way to manually cancel his ult and stop the channel?
Flash will cancel it, and it can be worth it if finishing the ult would result in your death as well. It can also be worth it if they literally only needed your shield to get a kill and you want to stay in lane to keep farming rather than let the enemy kill your tower. Also if you're in the team fight, just want to shield them, and still want to immediately get on a target that your teammate isn't near (ulti friend, flash towards enemy carry and taunt).
Teleport has an interesting effect depending on when you cast it. One possibility is that you shield your target, never appear there, and instead teleport to a different location. They still get the full effect of your shield. If cast where they both end at the same time, you will provide the shield but you'll stay exactly where you are, never teleporting anywhere. This can be useful if you decided a little bit late that it was a bad idea to ulti in and you planned on teleporting somewhere else anyway (say you just went back to heal up and planned on teleporting to lane).
Cleanse does not stop ult (can cast during ult)
Zhonya's Hourglass does not work (can't cast it during ult)
Quick Silver Sash does not stop ult (can cast during ult)
Ghost does not stop ult (can cast during ult)
Besides kindly asking an enemy to stun/fear/knock you up (etc), I do not believe there is a way to stop you from teleporting to an ally, possibly part to how game changing Shen's ult is, and how Riot wouldn't want you to accidentally not save an ally or that it wouldn't fit with the theme of "standing united".