The only non-looping/non-map solution I could come up with is the code-assertion counting technique:

 ...
 #  the array positions of  the chars are viewed as 'bits'
 #  Bits:   1 1 1 1    ==> decimal 15
 my @a = qw'a r z x';
 use re 'eval';
 our $t = 1;     # $t will be modified within the regex

 # build the regex, essentially: /a(?{...})| b(?{...}) | c(?{...}) ...
+ /g
 my  $p = 0;     # position count variable during initialization
 my  $expr = join'|', map quotemeta($_)."(?{\$t|=".(1<<$p++)."})", @a;
                
 
 # initialize before run
 $t = 0; 
 my $mystring = 'areqrtyz';
 # evaluate the regex in list context () and 
 # look after the result in $t (comma operator =>, )
 print 'no match' if () = $mystring =~ /$expr/g, $t != 15;
 ...
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Regards

mwa