The whole "Chakotay died of a broken heart" meme was never actually stated. All the Admiral said was that "he was never the same after Seven's death."
Well, guess what, folks? When your spouse dies, you never are the same again. Doesn't mean you've given up on life, doesn't mean that you withdraw, doesn't mean that you're gonna die of a broken heart. It just means that you're never the same.
I was widowed 10 years ago at the age of 46. Yes, that death did change me.
ETA: As for the "it wasn't easy living all these years without her...," again I think the interpretation of one line has been taken out of context and grossly exaggerated.