Relay log rotation have nothing to do with it.
What's critical is that the slaves, if set up with
log_slave_updates (i.e. in themselves logging to binary logs), are pre-configured with
binlog_format = MIXED or
binlog_format = ROW.
To elaborate: there is no problem if the master uses
binlog_format = STATEMENT and the slaves use
ROW. There is a problem if the master uses
ROW and the slaves use
STATEMENT. You just can't restore the exact original statement from
Likewise, if you master is
MIXED, then slaves must be wither
Back to your question, assuming the slaves are already configured with
MIXED, there is no problem in just
SET GLOBAL binlog_format = MIXED on the master. There is no problem in the binary log containing some entries of this format and some entries of the other. There is no problem with the relay logs containing entries of both forms.
I disagree with the accepted answer you linked to.