Or is a good nylon faced gunsmith hammer sufficient?

You can use the hammer, but the round lead babbit bar is much better due to its weight. You just have to be gentler with the raps if you use the lead bar. Remember to use the tool that goes inside the yoke barrel, so you don't crush it.

By tool you mean the yoke/crane alignment tool, yes?

YOKE/CRANE ALIGNMENT TOOL | Brownells

Yes sir, that's the one.

If you insist on using a hammer, buy a small dead blow hammer.
A standard plastic hammer will bounce too much dissipating the force and making it hard to judge how much bend you're getting.

The babbitt bar is to have a heavy mass that won't bounce, and won't marr the metal.
You could also use a lead bar.

A plastic hammer is a non-starter. Don't.

Noted and thank you.

And if you use anything but a babbitt or lead bar, put a soft cloth around the cylinder to protect the finish.

Most babbitt bars I've seen in shops have been wrapped in electrician's tape; same purpose?

The two babbit bars that came in the S&W armorers kit were not wrapped in tape. I use them as they came. They do not mar the bluing or the surface.

does anyone have a tutorial or a video on fixing this gap?
i have a decent gap on my 625 that has always bugged me

Tape will pick up grit and dirt and can scratch the finish. A clean cloth won't.
It's the small details that separate a real pro from an amateur.

What gap??
Barrel-cylinder gap??

If you have too big a gap between the barrel and cylinder AND THAT'S THE ACTUAL PROBLEM, the only way to fix it is to have the barrel set back one full thread, have the barrel-cylinder gap cut to the proper size with a special tool, have the forcing cone re-cut and gaged to the proper mouth diameter, and have the cone smoothed by lapping with a brass lap and valve grinding compound.

Also, you'll have to have the extractor rod shortened.

no it's the frame and yoke gap, looks like someone played movie gun and bent the yoke.
it didn't bother me too much until i got my 686-1 and saw what a nice hairline match up it had.

At some point in the past, S&W stopped worrying about the size of any gap between the frame and the yoke.

If the assembly is properly working and there's no major movement in and out of the frame, a gap is considered not to be an issue.
If the gap is significant?? and/or there's "too much"?? movement, then it should be inspected.
The key questions are, if the gun in time, proper cylinder-bore alignment, and isn't sprung or loose, a gap is okay according to S&W.

Like everything else in the world, standards that used to be unacceptable are now considered to be normal.

This whole thread gave me a reminder of my Master Armorer's Class from S&W. The 'final' exercise was to take a furnished revolver that had its frame/barrel and yoke all bent out of specifications. Each of us had to bring the revolver assigned to us back into specifications using only the Babbitt Rod, Range Rod, poly wedge and Yoke alignment tools along with the usual feeler gauges. Thru my many years as a handgun gunsmith, I never had to correct anything that radical until just recently, I acquired (very cheaply) a pre-Model 10 that had been run over (?) at the shooting range by the previous owner. He never did quite own up to how that happened.

Anyway I got out the above tools and went to work. An hour later I had a revolver that was back into specs and was worth three times what I paid for it. :-) ............. Big Cholla

Well done.

Gunsmiths sometimes have a bit of a viscous streak that often manifests itself as trying to pin down a gun owner on EXACTLY what happened.

Oh, the stories........

Another story :-); I was working part time in a gunshop in Denver,CO many years ago. It was part owned by a very nice single lady. She shot weekly in her range using the shop's guns. She carried a short barreled S&W M 19 loaded with Super Vel. This was before 'concealment' purses, so she carried it in the bottom of her huge carry-all purse. The night came when she got home she realized that a light was on in the back of the house that was not on when she left. She opened the door and a very tall naked man came striding down the hallway towards her. She had the M 19 in her hands by this time and yelled at him to stop. He didn't and she fired one shot. By her explanation, the handgun just blew up and caught fire. The shot missed but the man ran to the back of the house and jumped thru a glass window pane cutting himself rather badly. She dropped the handgun and called the police. They had the guy within 20 minutes. She brought the handgun in to us in the gunsmithing department and asked us to check it out. We did so and found nothing wrong except it was extremely sooty. After looking at the bottom of her purse and asking when she last cleaned the M 19 we determined that she had NOT cleaned the gun or shot in over two years. The debris and lint collected in the gun barrel and around the cylinder must have burst into flames. Plus Super Vel was noted for a huge muzzle blast of flame under low light. After that, we took it upon ourselves to clean her revolver once a week unasked. ........... Big Cholla