Unfortunately, that only works for ~/path. The ~ form also works as ~user2, meaning the home directory of user2, not the current user's home directory.

Something more complete might look like this: Warning: untested code

my $filename = "~user2/tmp";

if( $filename =~ m@^\~([^/])+@){
     my $home = (getpwnam($1))[7];
     if( $home){
          $filename =~ s@^\~[^/]+@$home@;
     }
}else{
     $filename =~ s@^\~@$ENV{'HOME'}@;
}
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This should handle both cases.