How unsafe is it to change the data source of repl_distributor on a publisher
Know this is an old question but we've just been working with this, Last month we had to move our distribution server to a brand new machine, (Setup is two machines in AG stand alone distributor and a reporting server)

The only real way we found to move distributor server is to completely tear down and rebuild replication, this can be done with right clicking replication and generate scripts

bare in mind you'll need to do this on the publishers and the new distributor.

We've just had an issue where our AG group didn't take the distributor change, and since its a read only node we're doing some experiments with different ways to do that, 

our tests of updating the [master].[sys].[sysobjvalues] table (which is where the 'datasource' value is actually stored (the sysservers is just a view) have resulted promising results if you want the server to never work ever again.  Tearing things down and rebuilding it is painful, but its by far the safest thing to do.

Ste