Would you trust a reputedly secure file sharing service for public key distribution? In my context, I cannot use certificates. Key servers seem to require PGP/GPG formats yet I'm using Microsoft CngKey format in my app, hence this question.
Yes and No
You could print your public key on a billboard in the middle of New York and it would not cause you any problems, however, no one would be able to verify that the billboard in question was actually your doing. Further, if someone had write access to that billboard and changed the public key it would cause you headaches.
Something that you might consider is to stash the key in a Github repo owned by you ... this, while not 100% secure, would be far more reputable than a public dropbox link.
It's a public key. The whole point is that - it's meant to be shared.
I could send it to the government. It wouldn't make any difference. You use your private key for decryption. Keep that safe.
I recommend that you read this answer to understand the fundamentals.