Perhaps something like this using a virtual event:

#!/usr/bin/env perl

use strict;
use warnings;

use Tk;

my $mw = MainWindow::->new();

$mw->eventGenerate('<<FakeF1>>');
$mw->eventAdd('<<FakeF1>>' => '<F2>');
$mw->bind('<F1>' => [\&f1_callback, Ev('%k')]);
$mw->bind('<<FakeF1>>' => [\&f1_callback, Ev('%k')]);

MainLoop;

sub f1_callback {
    printf "F1 callback generated with %#x\n", $_[1];
}
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When I run this and press F1 followed by F2, I get this output:

F1 callback generated with 0x43
F1 callback generated with 0x44
[download]

Those methods are documented in Tk::event and Tk::bind.