If you're simply changing the connection string from one server to the other, then double hopping won't be a problem. Your connection would be going directly to the other server (it won't be authenticating to the first), so there is no opportunity to double hop.

Normally, if you have haver two locations to get data from it is better to have two data sources, rather than one and editing it. If you actually create a proper data source from scratch to the other server in your SSRS portal, rather than amending the original, does that work?

Edit: It would, also, however, be worth asking your network team to check that Kerboros is enabled between your two servers, just in case. I can''t guide you on that bit though, as it's not something I know how to do myself.