I'm wondering if the OP has ever seen a dead body, either in situ or at a morgue. The bodies that you see at a funeral service are heavily made up and don't really resemble a natural body. It's like an actress made up for a photo shoot and what she looks like when she wakes up. This assumes a body that is showing no decomposition.
However, a variation on the OP's second proposal could work out very nicely. But it can't be based upon facial recognition. I've seen dead family and friends and have even done confirmation that the body in the coffin is the correct body. Yes, they're the same, but they're not. The less work that has been done on the body the more noticeable this is. The classic eyes closed and jaw shut is not necessarily natural. My grandmother, in death, had an angry expression that I'd never seen from her. Considering she died while being snowed with morphine, I doubt she was angry when she died. (I doubt she was even aware of her death.)
Bodies in a morgue are always in their natural state, which may include significant animal, weather, and decomposition deterioration.
However, as Siri Karpal points out, tattoos can be a wonderful identification method. But you need to understand how a tattoo is used for identification. Tattoos have identification points, such as "a picture of an eagle, approximately three inches tall, with wings extended, and facing to the right" located on "the left bicep, approximately two inches above the elbow." This works well with most tattoos, as they are a recognizable image, and even abstract images are so frequently used repeatedly that they have identification.
This information is recorded during the autopsy and pictures are taken. If you file a missing person report, the authorities can check against the registry of dead bodies. In other words, your missing person has an eagle tattoo. If you don't have a picture showing the tattoo, then the authorities can show you pictures of tattoos found on bodies that are consistent in their biometrics to your missing person. This process has a fairly high success right.
However, every so often, a tattoo defies description. I remember one that was described as a splotch, consisting of several colors, with size and location recorded. These are next to impossible to figure out how to describe in a way that other people can see and recognize. Damage to the tattoo can increase the problem.
So I could see a morgue worker remember a unique tattoo and recognizing it on a bottle of honey. Understand that a body with a large number of tattoos would not meet the criteria here. It would have to be one tattoo, impossible to describe in any sort of meaningful way. You'd have to understand tattoos for this to make sense. I'd find that believable.
Jim Clark-Dawe