Well, real personal and subjective, but I'll try to answer.
After reading your question I went out into the backyard and shot a mag, trying to listen specifically for hammer noise. My gun is a .22/60.
1) Any hammer noise was quieter than the little 'snap' from the muzzle, which wears no further moderation (OEM condition). Obviously may be different with a 450mm barrel;
2) The round smacking the target was louder than any muzzle report or hammer/shot cycle noise. Target box consists of: paper target taped to cardboard, backed by black foam squares (from pellet shipments), then hitting tire treads cut from an RV tire, and finally backed up by a steel plate (but nothing normally penetrates to the steel plate).
3) If I can explain the noise from the hammer hitting the valve... You know that when you are in a canyon which echos, the sound kind of fades out - ECHO - ECho - Echo- echo... Well the hammer has just a little metallic ping, but it is like you don't hear the first or loudest part. Like PING-PINg-PIng-Ping-ping, but you don't hear it until maybe the 3rd level of 'loudness' and it then just fades off.
Not as quiet as some guns, but then again it is a smaller gun putting out 46 FPE at the muzzle. Not at all objectionable in any way to me. YMMV
Sorry but I have not shot a Cricket BP to directly compare.