I'm in favour of making changes for a variety of reasons. I'd change something that could be offensive, not because I mind offending, but because something that rings out as offensive in the current context can skew the balance of the song.
I'll change the sex of the parties in the song if it makes sense to do so - and sometimes it can add a new twist to a song. I heard Courting is a Pleasure sung as a man - but it has a different flavour sung as a woman. I prefer to sing the latter. However, Flora (a similar-ish song about betrayal) I wouldn't feel happy to change, and it doesn't bother me at all to sing it - I think it is quite obvious to the audience when a female is singing 1st person as male & hence singing about still loving 'her' is not incongruous.
Another song I've adapted is Banks of the Ohio - in which a vengeful woman kills her lover 'I'll let no man take liberties, if he will not then marry me'. I don't think a variant hurts the original at all.
I'll also change lyrics if they don't scan with the way I sing the tune.
I'll also make up some words if I don't know a whole song, or add/chop verses if the song seems too short/long.
For me it is more important to sing than to exactly reproduce a song.
For the particular song under discussion I personally would sing it as it is - but if you are happier singing a changed version then go for it. There is nothing worse than trying to sing something that bothers you in some way - it restricts the flow.
In general I'm heavily in favour of changing things for whatever reason applies. I like to hear variant tunes and lyrics - its part of what makes a performer/performance individual.
I dare say there are bad variants, but then there are bad 'reproductions' as well.

kris