join "|", map { "\\b$_\\b" } reverse sort keys %cats;
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I'd suggest putting a quotemeta in there, just to play it safe. Although I agree that using a proper parser is better! skooma: See also Building Regex Alternations Dynamically.

use warnings;
use strict;
use Test::More;

my %cats = (blackcat=>5, whitecat=>10,orangecat=>20);

my ($regex) = map { qr/\b($_)\b/ } join '|', map {quotemeta}
    sort { length $b <=> length $a or $a cmp $b } keys %cats;

diag explain $regex;

sub do_replace {
    my $input = shift;
    $input =~ s/$regex/$cats{$1}/g;
    return $input;
}

is do_replace("log10(blackcat)"), "log10(5)";
is do_replace("log10(blackcat)*whitecat*(log10(orangecat))"),
    "log10(5)*10*(log10(20))";

done_testing;

__END__

# qr/\b(orangecat|blackcat|whitecat)\b/
ok 1
ok 2
1..2
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