It looks like William had another wife, either legal or common law. Her name was Sarah (possibly tge Sarah on the death certificate)
Sorry to bring this up again, BUT
You state that William appears to have another wife, legal or otherwise. BUT the marriage between William Shackleton and Sarah Waterhouse took place in
1841. The marriage between William Shackleton and Rose Hindle took place in
1848, therefore IF there is an illegal marriage it is between William and Rose - I don't, personally, think that that is the case, as I believe that we have two individuals named William Shackleton, who married two individual brides.
All the documentary evidence points to the burial in 1851 as being William who married Sarah - he DOES appear on the 1851 census with Sarah, he is said to be 29 years old on the 1851 census, and is said to be 30 on his burial in May 1851, informant on the death certificate is SARAH. The only discrepancy might be that he said he was "full age" when he married.
Rose, on the other hand, excluding the fact that she appears on the 1851 census as a 29 year old male, is said to be a widow(er), which implies that William has died prior to the date of the census.