Your code should work already. I tried it and got the expected results.

use strict;
use warnings;

my $newUser ='$dummy';
while (<DATA>) {

    s/O_PREFIX=\w+/O_PREFIX=$newUser/;

    # s/(?<=O_PREFIX=)\w+/$newUser/;

    print;
}

__DATA__
if [ $YOU = 'frog' ]
   then
     export OUSER=TNN
     export CAR=SWs
     export O_PREFIX=ss
     export OS=corvette

fi
[download]

And the output -

if [ $YOU = 'frog' ]
   then
     export OUSER=TNN
     export CAR=SWs
     export O_PREFIX=dummy
     export OS=corvette

fi
[download]