#! perl -slw
use strict;
use Data::Dumper;

my %map = map{ split /=/, $_, 2 } split /\n/, do{ local $/; <DATA> };

print Dumper \%map;

while( <> ) {
	chomp;
	if( m[http://([^/]+)/(\W?)]i ) {
		next unless defined $map{ $1 };
		substr( $_, $-[0], $+[0] -  $-[0] ) =
			'http://' . $map{ $1 } . ( length $2 ? $2 : "\n$2" );
	}
	print;
}

__DATA__
www.theirsite.com=our.server1/theirsite/
www.dummy.com=our.server2/dummy/