One thing I can think of is an overzealous corporate security solution blocking or holding back your email purely for having an attachment, or because it misunderstands/presumes the cipher-looking text file to be an attempt to bypass filtering.
Other than that might be curious questions from curious receivers of the key/file they may not understand, and will not be expecting. (“What’s this for? Is this part of the contract documents? Oh well, I’ll forward it to the client anyway”)
Other than that it’s a public key, go for it. Hard (for me anyway) to decide to post them to public keychains when the bot-nets read them for spam, so this might be the next best thing?