I believe Jesus shed all His blood for our sins, and not only our sins but the whole world.
(1 John 2:2 And He Himself is the propitiation for our sins, and not for ours only but also for the whole world.)
Luke 24:39
Behold My hands and My feet, that it is I Myself. Handle Me and see, for a spirit does not have flesh and bones as you see I have
No mention of any blood here, though this isn't exactly evidence He had no blood, just the fact He didn't mention it.