It seems to me that most men get grey hair in their beards either before or at the same time as grey hair on the head. So some grey on the head and no grey in the beard would look rather weird to me. Also, most 61 year olds look old enough that some grey hair - especially in the beard - is expected, and hair dye is obvious, and doesn’t often look all that good, since it’s rather obvious that it’s dyed. I’d like to think that this doesn’t play a role in companies deciding to hire qualified employees, but unfortunately, I think it does, and I think that in many men, hair dye is obvious enough that people may react negatively to it.
Then again, dying a beard doesn’t cost all that much, and if it looks weird, you can always go with option #2 which is to shave it off anyways! So despite my first paragraph, I say go for it, see how it looks, and go from there, assuming you are willing to shave the beard in the first place!
I’m also a little hypocritical, as I dye my hair, though I’ve done so continuously since I was 15 because I hate my natural colour and I’m (only) 30. I have no idea how much/or any grey hair I have! Though to, I guess, reiterate my first paragraph in different words, a man with salt and pepper hair and a grey beard looks normal to me, and, often, good.