Wow.. The DMM seems like it's always on sale for $2.99 or $3.99 at most.. you just picked the wrong week I guess to need one . Oh well, at least you didnt waste more money at RadioShack.
Yes, swapping tubes is the same on an arcade chassis or an 8liners chassis. Steps, in order are:
1) Unplug (duh)
2) Discharge and remove anode wire. (Most dangerous..google for the safety issues/how to do it)
3) Remove ground wire from neckboard that leads to wire touching the back of the tube
4) Check for silicone caulk or glue adhering the neck board to the tube. If so, use a SHARP utility knife to carefully cut the seal.
5) Remove the neckboard by pulling straight off the back, using as little side to side pressure as possible.
6) Find the yoke wire and disconnect from the chassis.
7) Find the degaussing coil wire and disconnect it from the chassis if socketed. If soldered you can choose to simply pull the tube out around it leaving it in place.

Remove the 4 bolts holding the tube to the TV case or to the arcade frame
9) Remove the tube from the case or frame.
Now simply swap the tube with attached yoke to the other . Do not bring the TV's deguassing coil over. Use the original one that came with the arcade chassis. (They *should* be the same, but there is no need to swap just in case there is a difference and the original one still works)
Just reverse the order to reassemble. Ensure you get the yoke plugged in correctly or you can fry the yoke or the circuitry. (It should be keyed so one connection is farther than the other 3).
LMK if you need assistance.