My understanding is that if you're not configured with VPN then you're not truly mining anonymously. But since you're not sending your BTC directly, the transaction is not recorded in the blockchain either correct? Since you're donating your hashrate to a dedicated pool provided by Slushpool, is there anyway, other than from Slushpool themselves, for anyone to actually see that your particular Antminer is being used to donate to that cause?
It's not easy to track you, but you are not 100% safe, and here is why, once you establish a connection with the pool, your ISP might perform an Eavesdrop attack on you, the worker/account name will be in those packets which you exchange with the pool, it's not like the Stratum protocol will send all these info in plain text, but there is no guarantee that nobody can see what's happening.
These kinds of attacks are not so easy to perform, and chances are, they will usually be targeted to actually work, but I don't know how much effort and money your ISP is spending to look at things like that.
I think it's a lot safer if you just mine to your own address or use a new address which you own, withdraw the coins to a solid mixer, use the mixed tokens to directly donate to that "country that is in need of help".