String::Interpolate might be useful in this task. If you move your variables to be interpolated to a hash, you will be able to do it yourself, like this:

my %variables = ( ... );
...;
while (<FILE>) {
 s/\$(\w+)/$variables{$1}/eg;
 print;
}
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What you are writing looks like a templating engine. Unless it's a "homework" question, it might be useful to look at Text::Template, Mason and Template.