It still looks to me like the exec is the problem:

#!/usr/bin/perl

$SIG{INT} = $SIG{HUP} = sub {};
exec 'perl', '-e', '$span=5; $span -= sleep $span while $span > 0;
                    warn "Sleep is done\n";'
    or die 'exec failed';
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Hitting CTRL-C kills the process, and doesn't print Sleep is done, as it would if it had completed normally.

Of course, using do instead would work, because it would avoid the exec.

Does it even make sense for a signal handler to persist across an exec? A signal handler is basically an address in memory that the kernel should cause the user process to jump to if a signal arrives, but after an exec the address space will change, and the old address will almost certainly not be a sane place to jump to.