What you can do is use the Local::TeeOutput mod. This will allow you to open a connection set with different parameters and then close the connection to refer back to the original, before the open connection, parameters. It would be something like this.
use Local::TeeOutput;
openTee(*STDOUT, ">$LogFile");
select(STDOUT);
$|=1;
print "Something"
closeTee(*STDOUT);