What part would have been the hardest? I'm a Canadian and the only time in my life I had to swear an oath was when I went to work in Government. I think I was offered an option to swear on the Bible or to the Queen. Again, the only time in my life it came up and it was kind weird.
Americans swear alliegiance to their flag every day in school. That's weird.
The constitutional monarchy is just a leftover remnant and not relevant to daily lift. The Governor General (the King/Queen's representative) does have the power to dissolve and create governments but it's really just symbolic. If they were ever to use that power against the wishes of the electorate, that power would probably get taken away really quickly.
King Charles hasn't even visted Canada since he became king. That's how much the monarchy means to us too in Canada. Symbolic, but stay away.