I recall my son’s upsherin which was on 8 Tishrei, so the day before Erev Yom Kippur. For me it was harder doing the haircutting (and all of the activities associated with that – going to rabbonim for snips plus a festive meal) than it was to give birth at that time of year. I plan on splitting up the celebrations associated with his Bar Mitzvah in 2 years.
If Sunday is the day you want to do it, then I would suggest doing it the following week since doing it on erev RH, unless you are not making any meals in your house over those 2 days, would be almost impossible for your wife to enjoy.