Use goto:

use 5.010;
use strict;
use warnings;

sub foo { say "This is foo <@_>" }
sub bar { say "This is bar <@_>" }

sub call {
    my $sub = shift;
    goto &$sub;
}

$_ = "foo 123 foo bar bar 456";
while (/(\w+) (\w+)/g) {
    call $1, $2;
}

__END__
This is foo <123>
This is foo <bar>
This is bar <456>
[download]

Of course, that only helps to circumvent the no strict 'refs';. It doesn't solve anything that no strict 'refs'; tries to protect you from.

Adapting the trick so it works with your templating system is left as an exercise to the reader.