If you WANT to use RegEx then:

use strict;
use warnings ;


my @csv = <DATA>;

foreach my $line ( @csv ) { 
    my $clean_line = $line ;
    while( $line =~ /"(.*?)"/g ) { 
    my $match = $1 ;
    my $match_cleaned = $match ;
    $match_cleaned =~ s/,/~/g;
    my $location = index( $line, $match ) ;
    my $clean_line = substr( $clean_line, $location, length( $match ),
+ $match_cleaned );
    }
    print "$clean_line";
}

__DATA__
123,abc1,test1,"1,3,5",new,"abc,dfg,hj"
124,abc2,test2,"1,3,5",new,"abc,dfg,hj"
125,abc3*,test3,"*|1,3,5",new,"abc,dfg,hj"
[download]

Notice that replace withing $line is not done using a regex - this is to avoid escaping $match and to also speed things up.

You can compress this code but its been stretched out for readability.