Are there any exchanges that don't require photo ID, or other personal info, if no fiat currency is involved?
Only crypto in and out.
Try coinomi.com. AFAIK it doesn't require an ID to trade cryptocurrency pairs. Yobit also doesn't seem to require an ID. I have traded and was able to withdraw without giving any personal details.
I heard that Bittrex started to ask people to verify but I still have an account there which I can use in full and they haven't asked me for ID at all. Maybe it's only for new users.
Be careful with yobit though, there have been complaints lately with user's altcoins are stuck inside Yobit.
For reference
https://bitcointalk.org/index.php?action=trust;u=406594I tried to exchange my Bitcoin Cash into BTC a while back using Bitfinex and they didn't ask for verification, so I think OP can try that.
Bittrex on the other hand requires verification in order to withdraw, without it you won't be able to withdraw at all, so definitely not a go for OP.