Is it safe to delete replication relay-bin files?

I think a better answer is relay logs can be 'deleted' but mysql should manage it automatically. One way to do this is to check for the value of relay_log_purge.

It should be set to 1 if you want mysql to manage them:

set global relay_log_purge=1;

You would probably need to flush the logs:

flush logs;

This does not affect the binary logs.

Maybe try to resync your master and slave.

If possible, cleanup the slave by running a

reset slave

it will purge all relay binary logs.

Then set the replication again with change master to ... You may have too much lag between your master and slave.