I think the problem with Pasha is that
a) in English, -a endings are associated with girl names,
b) Pasha sounds a lot like Passion, which is pointedly sexy sounding, plus with a girly ending which seems extra weird (the connotation of giving a "girly-sexy" name to a boy being the strange thing, I think)
c) many people know Pasha as a chain of dodgy nightclubs. So on top of the girly-sexy connotations, you also have a dollop of "seedy" in there.
d) On top of it all, it's a nickname, not a full name.
So. TBH, as an English speaker, Pasha as a given name sounds girly, sexy and seedy. If you named him Pawel/Pavel and nnamed him Pasha, that would make more sense, because at least your son could choose to use his whole name in situation where his nn would embarrass him.
I know many Russians and if a Russian-accented, Russian-surnamed person went by Pasha, I wouldn't bat an eye. (Having said that, I have actually never met a Pasha... I know a single Pawel...)
But an English-speaking, non-EEuropean-surnamed child with the legal name of Pasha? I would think his parents were fairly short-sighted to name him that, tbh.
FWIW, in terms of honouring your DH's heritage, in Russian naming traditions it would be extremely rare to name a child by a nickname in any case. Kids are named with saints' names, always in full, to honour the saint and other family members with the same saint's name. Orthodox priests would wag their fingers at anyone who tried to shorten their child's baptismal name.
Hence nicknames being popular in Russia... to distinguish the 1000 Dmitris/Alexeis/Katerinas/Anastasias etc from one another.