$ perl -wle'use strict; my $str2 = "@cce$$ag@!n"; print $str2;'
Global symbol "@cce" requires explicit package name at -e line 1.
Global symbol "$ag" requires explicit package name at -e line 1.
Execution of -e aborted due to compilation errors.

$ perl -wle'use strict; my $str2 = "\@cce\$\$ag\@!n"; print $str2;'
@cce$$ag@!n

##</code><code>##

my $str1_pat = quotemeta($str1);
$str1 =~ s/$str1_pat/$str2/;

  - or -

$str1 =~ s/\Q$str1\E/$str2/;   # Same thing.