On this system we are not permitted to install any modules

Well then you will be stuck in quote-escaping hell as I see now you have a nasty mix of both double and single quotes there. This test looks OK:

use strict;
use warnings;

use Test::More tests => 1;

my $want = q{su - admin -c "psql -p 5555 mcdb -c \\"update ev_cus_prof
+ set active='f' where epid='INIT_EV_HIGH_PRIORITY';\\""};

my $PSQL = q{psql -p 5555 mcdb -c \"update ev_cus_prof set active='f' 
+where epid='INIT_EV_HIGH_PRIORITY';\"};
my $cmd = qq{su - admin -c "$PSQL"};
is $cmd, $want, "have $want";
[download]

But, in your shoes I would approach whichever entity has imposed the no-modules rule and point out that it means you have to ask the help of complete strangers on the internet to solve what would otherwise be a trivial task.