Oh my, where to start?
Do you have reason to believe the play head azimuth is out? If so, by a small or large amount?
The only reason to get azimuth spot on standard is if you are expecting to play your tapes on another machine, or to play theirs on yours. Normally, for home recordists that's unlikely, especially these days. Apart from that there will be no sonic improvement in having your machine aligned perfectly to test tape azimuth standard. More important to have record and play heads aligned to each other, even if absolute azimuth is not spot on.
Even if for perfection's sake you still want to adjust the azimuth from what it now is, and if the head has a tape wear groove, the standard advice is, dont until you relap or replace the head. After that you should certainly adjust azimuth. Tape wear grooves are like tram tracks. They lock the tape into tracking one way. You cant reliably change the azimuth even if you wanted to.
OTOH your heads may have recessed slots at the edges of the tape path, and possibly in that case it would be OK to readjust azimuth, so long as the tape wear hasnt got down to the level of the bottom of the slots and/or the tape never was centred properly and it has left a ridge on one edge anyway. In that case, relap or replace.
A scope/cro/ is NOT essential for azimuth alignment. You can do it quite reliably with a meter that can handle the azimuth frequency, often even the machine's own VU's. Adjust coarsely first for maximum deflection on all channels. Then sum say channels 2 and 7 and very carefully adjust a small amount either side of this for the maximum average reading. This last adjustment will be very critical, but will be of benefit if you ever record tracks which have the same material recorded on them and you sum them.
You can get into cro's, lissajous figures, X-Y inputs if you like but you will likely get no better result, just pretty pictures on a screen. You can even use a single trace cro and just sum tracks 2 and 7 into that one channel. But you dont even need a cro at all.
But standard advice is if the head is worn , dont even touch the azimuth.
Or at least just in case the machine's azimuth has been changed since the wear groove was formed and you just want it to play better, adjust azimuth for the best sound by aligning back to the wear groove.
I feel more emphasis here should be placed on tape head condition. It's pointless spending lots of time and money on aligning a machine unless the heads are in good nick in the first place.
Good luck, Tim