eval the replacement-string into a sub, and apply just one /e at the s///

  DB<137> $rep = '<$1>'

  DB<138> eval qq( sub rep { "$rep" } )

  DB<139> p "abc" =~ s/(.)/rep()/rge
<a><b><c>
  DB<140>
[download]

This will give you more control about what is happening, since you can use B::Deparse to check the replacement string before executing it.

Like this you have at least a chance to reject dubious code.

  DB<140> p B::Deparse->new('-q')->coderef2text(\&rep)
{
    use feature 'current_sub', 'evalbytes', 'fc', 'postderef_qq', 'say
+', 'state', 'switch', 'unicode_strings', 'unico\
de_eval';
    '<' . $1 . '>';
}
  DB<141>
[download]