It can be done safely, but only if you're using only a TLS-encrypted HTTP to access the site (encrypting not just the credentials themselves, but the entire page they're on) and only if you're using a valid CA-signed certificate. Just before entering your credentials through the web proxy, make sure the certificate your browser is using matches the one you paid for. If there are any discrepancies at all, get the heck out of there.
TLS (formerly called SSL) is encrypted on the client and decrypted on the server using asymmetric public key cryptography. Assuming the web proxy returns a valid certificate signed by a CA (and assuming you haven't given the proxy your certificate's private key), the connection cannot be forged or changed in any way.
Even still, web proxies can be a little shady, so I'd recommend following Phoshi's advice anyways, changing your password afterwards just in case you make a mistake and leak some information.