Which way are you trying to Bair? Towards or away from the stage? Oh I think I get it. So you want to run off stage and, without jumping, Bair where people would be holding onto the ledge, but you want to do this while holding a nade. If that's the case, then this should be really simple. Pull out a nade, shield drop it, pick it back up, run off stage, as soon as you run off the edge put the joystick in neutral hit Z to Z-drop the nade then instantly catch it with Bair. You will Bair that section of the ledge while holding a nade and depending on the timing, it will explode and let you recover easier.
That is of course, if that's what you mean. This is all untested btw, but I see no reason why it shouldn't work.
If you meant something else then try to be a bit more specific and I'll tell you how to do it. And if I get the time, I'll test it for you. Actually...... I'll test it now. Just cause you're Luke XD. One sec.
(Don't you think it's funny how I always do this? Like I may as well re-write the whole post, but no, I have to do it this way.)
Ok so after a bit of testing, it appears that Snake can't do it the way I just mentioned because he drops the grenade too high above his head (Toon can do it though! I knew it was possible.) but just so I don't leave you without anything, I found three other ways to perform the Bair in that spot with a nade.
1. The obvious way. Pick up the nade, SH off the edge, ZAC with Bair. (You know ZAC right?)
2. The not so obvious way. Facing away from the edge, Shield drop a nade right on the edge, run off then Instantly Bair (C-stick is easy for me). Works fine but there is that set up time that you have to worry about.
3. The inspired way. Roll all the way to the edge so pretty much you need to be as far over to the edge as possible facing away from the edge, Pull out a Nade, Shield drop it so it falls off the edge then Instantly let go of shield (Just tap shield) and run off the edge (You're right on the edge, so it's really just a step off the edge, not a run.) Then Instantly Catch the Nade with Bair. I like this way, it's quick, relatively easy except for the Instantly run off, Instantly Bair part, because you need to do it quick enough so you can catch it. But as it is, I was only testing for 5 minutes, and of that 5 minutes, about 1 of them was doing this way, and I can already do it easilly. So yeah, it's relatively simple, so simple, it must be known already. Well you tell me, you're the Snake main.
But that's all I got. If you didn't like them or I'm talking about something else, then hopefully these will give you a few ideas. It's just such a shame that it couldn't be done the original way, but oh well.
Cya man!