David...
It's a bit of a handicap, but not much of one, I'd suggest, as long as you can grip the guitar neck with the left hand. As mentioned above, it's not 'best practice' to use the thumb for playing, or muting, the sixth string (the low 'E'...). No longer having that option won't prevent you playing all the rest of the guitar styles. Just pick it up and play, as most of us did, and keep 'Ol' Stumpy' on the middle of the guitar neck, in true traditional manner.
The notion of going 'lefty' is not daft, though; there are many lefty guitarists who play 'righty'; it's simply a question of doing it; it becomes natural quickly enough. I have a brother, a hard lefty, who picked up my righty guitars at first, and was very soon playing far better than I was. His 'dominant' left hand was much more dextrous with chords and fingering, so I know that it can be successful. It would be to your advantage to try this out as soon as possible, though, and stick with it; it's not so easy changing once the brain has decided what each hand does.
Good luck with your decision, whichever way you choose to go; neither are an obstacle to becoming proficient. I'd add my usual encouraging phrase, useful in so many circumstances...
'It's the first forty years that are the hardest, after which things sometimes tend to get slightly better.'
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