Is there anything wrong with getting a haircut on Motzei Shabbos (Saturday night)?
I believe the reason it is said that its best not to get a haircut on Motzei Shabbos is because of the following: it is a nice thing to get a haircut on Friday to honor the approaching shabbos. If you wait till Motzei shabbos, it is embarrasing to shabbos because you didn't do it before and you are doing it right after. Therefore, it is probably better to wait until Sunday.
This would probably apply to shaving as well.
In a discussion about whether cutting hair on Friday when Rosh Chodesh Sivan is on Sunday is similar to when Lag Baomer is on Sunday, R. Shlomo Kluger makes the following point:
Chochmat Shlomo O.C. 493:2
ובפרט דבזיון הוא שעל שבת לא יגלח וביום אחד אחר השבת יגלח
And particularly because it is disgraceful that for Shabbat he didn’t shave but on Sunday after Shabbat he did shave.