I was able to piece together a solution (I think), based on someone's code I found on SO:

use NativeCall;

constant BYTE    := uint8;
constant WCHAR   := uint16;   
constant DWORD   := int32;    
constant REGSAM  := int32;
constant WCHARS  := CArray[WCHAR];
constant BYTES   := CArray[BYTE];

constant HKEY_LOCAL_MACHINE = 0x80000002;
constant KEY_QUERY_VALUE   = 1;
constant ERROR_SUCCESS     = 0; # Yeah, I know. The Win-Api uses 0 for
+ success and other values to indicate errors

sub RegOpenKeyExW( DWORD, WCHARS, DWORD, REGSAM, DWORD is rw) is nativ
+e("Kernel32.dll") returns DWORD { * };


sub RegQueryValueExW( DWORD, WCHARS, DWORD is rw, DWORD is rw, BYTE is
+ rw, DWORD is rw) is native("Kernel32.dll") returns DWORD { * };


my $key = 'SOFTWARE\Microsoft\Windows\CurrentVersion\App Paths';

my DWORD $hkey;
my $length = 1024;

sub wstr( Str $str ) returns WCHARS {
    my $return = CArray[WCHAR].new( $str.encode.list );
    $return[$return.elems] = 0;
    return $return;
}

my $h-key = RegOpenKeyExW(HKEY_LOCAL_MACHINE, wstr($key), 0, KEY_QUERY
+_VALUE, $hkey);
say $hkey;
[download]

The $hkey reports back a 3 digit number. However, it changes with each run, so I'm not sure if it's running correctly.