you can do it like this:
(a) first splitting the input string into complete records with (xCXX /A)*, (this skips the type, reads the length byte, goes back 2 bytes, and uses the length to read the record)
(b) then for each record extract type and string map { unpack "CxA*", $_ } (this reads the type, skips the length byte, and reads the string of the record).

use strict;
use warnings;

my $inputString = "\x03\x04Hi\x43\x08Hello!";

my %myDict = map { unpack "CxA*", $_ } unpack "(xCXX /A)*", $inputStri
+ng;

print "$myDict{0x03}\n";  # "Hi"
print "$myDict{0x43}\n";  # "Hello!"
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[edit]
better wording: chopping -> splitting
Your code created an extra entry in the hash (type = 0x30, empty string) because of the appended "00".
[edit2]
Incorporated the hint from AnomalousMonk (thanks!)