Strain if you must, but as I said gravity has already taken care of that for you. As long as you leave the last 3/4 in. or so of liquid in the fermenter you're golden. If you use a secondary you're even better. I'm not even counting on the fact that the glass in a hydrometer is so thin that you could probably chew it without injury.
I would have no problem drinking your beer. You can even send it to me and I'll prove it.