I have a mixed opinion on the wearing of hijab. As far as the original question, no I would never wear it because I'm a man.
People keep making comparisons between Christianity and Islam and the enforcement of dress and strict lifestyles. They seem to be making their own arguments against themselves sometimes because they mention covering the head and wearing the wimple like Christian women did in the Middle Ages, unintentionally pointing out that Christianity has progressed beyond this time while Islam in some areas has not.
Even many nuns these days no longer wear the habit in America, I'm not sure how common that is in some other countries. It depends on the particular order of nuns I believe.
On the other hand, I've got to know and worked with many women who do wear the headscarf and I've also known women who were practicing Muslims who don't wear it at all. Some Muslim women argue that it's not required although I think this is a minority opinion. In both cases I didn't get the feeling they were especially oppressed or that wearing it made such a difference to that.
In many Muslim countries women don't have as much freedom because of the family's reputation, like if she goes out alone at night or smokes in public or drinks or marries someone her family doesn't approve of (this last one can apply to men as well) then the family's reputation suffers and it's a problem, so this is restricted. But wearing a headscarf doesn't necessarily mean these restrictions go away.
I've heard from Saudi women's activists that wearing the veil is actually low on the list of priorities and some of them don't mind it. Getting rid of the guardianship system that legally puts male control over women's ability to travel abroad among other things is higher up.
I know many people could bring up isolated instances of extremist Christians identical to what we see among extremist Muslims but I think this is largely irrelevant. Christianity doesn't have nearly the power that Islam has in the 21st century. That's a bold statement and I agree Christianity has a lot of political power but not like Islam.
But to go back to some statements in this thread - I don't think even in Iran or Saudi Arabia that women face the death sentence for not wearing hijab. I think that would only happen in al-Qaeda or ISIS controlled territories and even then maybe they would just apply some other lesser punishment. And almost all Muslim majority countries don't legally mandate it. I think in the city I live in, about 40% maybe don't wear it. You almost never see women in niqab here.
While it's true that the hijab can be a symbol of sexist oppression, it's got more to do with the theocracies (which the US installed) than the religion itself. So don't go thinking of Muslim men or Islam the religion as any more sexist than other men or religions, just recognize the fact that conservative theocracies are repressive towards their citizens by nature. Plus for many Muslim women headdresses are just sort of part of their way of life, as much as you or I would consider wearing any article of clothing, there's just an Islamophobic trend in modern thought that falsely attributes some over-representative examples of violence against women to an entire culture and religion.
I guess you're talking about Mossadegh and U.S. support for Saudi Arabia but honestly I think to suggest the U.S. installed those theocracies (only in Iran would it be a literal theocracy I think) is a real exaggeration.