The juvenile North Atlantic right whale was caught in 1907 and has been in storage for six years.
The deceased Sowerby's beaked whale is "a rare sight on the Thames Estuary".
The Indian Ocean site is "far beyond anything we had imagined", one researcher says.
The museum in Hull city centre is due to reopen in August following a £20m, five-year renovation.
"Timmy" was found dead off the coast of Anholt despite multiple attempts to rescue it.
The minke whale was reported to Cleethorpes Wildlife Rescue (CWR) on Wednesday evening.
The Humpback surprised the fisherman in the sea of Brixham in Devon.
Tristan Northway, known on social media as Mr Fish, described the moment as "breathtaking".
An environmental team want to move the whale from Anholt to the Danish mainland, but they have had to pause the operation.
