Simply putting Tcl\bin first in %PATH% ought to suffice

I think that would mean that everything that wants to load zlib1.dll will then load the one that's in Tcl/bin.
What if there's something that needs to load the other (different) zlib1.dll ? It may now break - a somewhat unlikely scenario, admittedly :-)

If you want to ensure that Tcl/bin/Tcl.dll (and nothing else) loads that C:/Tcl/bin/zlib1.dll you can:
1) Copy C:/Tcl/bin/zlib1.dll to, say, C:/Tcl/bin/zxxxx.dll;
2) In C:/Tcl/bin/Tcl.dll, change every occurrence of "zlib1.dll" to "zxxxx.dll". It's best to do this second step programmatically, and to keep a backup copy of the original Tcl.dll in case something goes awry.

This hack (which I've used many times, though not with Tcl) ensures that the Tcl.dll will load zxxxx.dll instead of zlib1.dll - so it doesn't matter how many zlib1.dll files are in the path.

However, you can't just pick *any* arbitrary name for the zlib1.dll copy - the name of the copy must contain the same number of characters as the original.
That is, for this particular dll, the name you choose must consist of exactly 5 characters - it doesn't matter what those characters are, so long as they are valid filename characters.

Update: I probably should give some sort of indication of the program I would use to effect this hack. This is untested:

use strict;
use warnings;
use File::Copy;

File::Copy::copy('Tcl.dll', 'Tcl.dll_bak') or die $!;
open my $infh, '<', 'Tcl.dll' or die $!;
open my $outfh, '>', 'Tcl.dll_new' or die $!;
binmode($infh);
binmode($outfh);
while(<$infh>) {
  $_ =~ s/zlib1\.dll/zxxxx.dll/g;
  print $outfh, $_;
}
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Then check that Tcl.dll, Tcl.dll_bak and Tcl.dll_new all exist.
If they do, remove Tcl.dll and rename Tcl.dll_new to Tcl.dll.
If they don't exist .... freak !!

The actual code that I would be using does all of the removing and renaming, too.
And it does some stuff with permissions - though I'm not sure whether that's generally necessary:

close $infh;
close $outfh;
my $mode = (stat('Tcl.dll'))[2];
my $newmode = $mode | 0220;
chmod($newmode, 'Tcl.dll');
unlink 'Tcl.dll';
File::Copy::copy( 'Tcl.dll_new', 'Tcl.dll') or die $!;
chmod($mode, 'Tcl.dll');
unlink('Tcl.dll_new');
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Cheers,
Rob