#!/usr/bin/perl

use strict;
use warnings;

my %ersetzungen = (
    hans => 'Hallo',
    test => 'Welt',
);

my $datei = 'Ein Test: $hans $test.';
my @platzhalter = $datei =~ s/(?<=\$)(.+?)(?![A-Za-z0-9])/$ersetzungen{$1}/g;
print $datei;

The regular expression:

(?-imsx:(?<=\$)(.+?)(?![A-Za-z0-9]))

matches as follows:
  
NODE                     EXPLANATION
----------------------------------------------------------------------
(?-imsx:                 group, but do not capture (case-sensitive)
                         (with ^ and $ matching normally) (with . not
                         matching \n) (matching whitespace and #
                         normally):
----------------------------------------------------------------------
  (?<=                     look behind to see if there is:
----------------------------------------------------------------------
    \$                       '$'
----------------------------------------------------------------------
  )                        end of look-behind
----------------------------------------------------------------------
  (                        group and capture to \1:
----------------------------------------------------------------------
    .+?                      any character except \n (1 or more times
                             (matching the least amount possible))
----------------------------------------------------------------------
  )                        end of \1
----------------------------------------------------------------------
  (?!                      look ahead to see if there is not:
----------------------------------------------------------------------
    [A-Za-z0-9]              any character of: 'A' to 'Z', 'a' to
                             'z', '0' to '9'
----------------------------------------------------------------------
  )                        end of look-ahead
----------------------------------------------------------------------
)                        end of grouping
----------------------------------------------------------------------