'Chinaman' is an old-fashioned term but should be ok. It is generally not even used as an insult or in a derogatory way.
There are some racially derogatory names that refer to Chinese people (on the flip side, there are some Chinese terms that refer to Europeans in a racially derogatory way) ... but 'Chinaman' isn't one of them.
I guess it is in the ear of the hearer - this is the problem, how do you legislate for intentions or for people's feelings? It's ridiculous.
Also, acceptable racial terms go in and out of fashion like clothes.
E.g. in the US, negro was replaced by colored person. The NAACP stands for the National Association for the Advancement of Colored People. Then colored was considered offensive and so it was replaced by black or mixed race (depending on background). Recently, people of color has become a la mode, but I'm not sure why. All it tells you is that the person it's referring to is non-white - they could be black, mixed race, Indian, Aborigine, etc., and it's very closed to colored people, which is still considered offensive.
Confused? Well, I think it's the intention of the race industry people to keep people off balance and confused. That way, there are more opportunities for ordinary people to fall foul of this crap and be called racist.
BTW, every black person I've encountered has used the term black when referring to themselves and others.
If you can make sense of all this, I'm a goddamn Chinaman.