That's a very good catch by otter5 and I suspect that information is very likely to relate to your target people, and is more than a coincidence, for two reasons, several different but related pieces of otter5's information match or are very similar to your original information, and also because there are no WW2 USN muster records for Tim or Timothy Hahne, but there is one, and only one, series of muster records for the name of Charles Eugene Hahne.
As regards applying for his service record if you still need to do that, the muster list is very useful because it gives his ranks, enlistment and reenlistment dates, and his service numbers, and he had two numbers.
You said that he and your father served together in WW2, perhaps the names of Charles E. Hahn's WW2 ships may ring a bell with you.
Battleship USS New York BB-34
http://en.wikipedia.org/wiki/USS_New_York_%28BB-34%29Stores Ship USS Yukon AF-9
http://en.wikipedia.org/wiki/USS_Yukon_%28AF-9%29Cruiser USS Savannah CL-42
http://en.wikipedia.org/wiki/USS_Savannah_%28CL-42%29Carrier USS Bunker Hill CV-19
http://en.wikipedia.org/wiki/USS_Bunker_Hill_%28CV-17%29Minesweeper USS Penetrate AM-271
http://en.wikipedia.org/wiki/USS_Penetrate_%28AM-271%29*******************************************************************************
Charles Eugene Hahne service number 268 23 80 enlisted 18th August 1936
In 1939 he was on board the New York he is a Seaman 1st Class, probably his first or second ship, he arrived on board 7th April 1937
In 1940 he transferred to the Yukon he is a Quarter Master 3rd Class
Whilst on board the Yukon his period of enlistment must have expired because on 13th September 1940 he reenlisted at Portsmouth Virginia for a further enlistment period of 4 years and he continued to serve on board the Yukon.
In his September 1940 Yukon muster list entry they wrongly listed the first three digits of his service number as 269 instead of 268.
He served on the Yukon until 1942 by which time he was a Quarter Master 2nd Class
In 1942 he transferred to the Savannah as a Quarter Master 1st Class
In 1943 he transferred to the Bunker Hill as a Chief Quarter Master Anti Aircraft
In 1940 he transferred to the Penetrate as a Bosun he has the same 13th September 1940 enlistment date, but he has a new service number 326728 possibly that was his number as an Officer because the muster list has an additional entry for him which says that as an Officer he was transferred for treatment on November 12th 1944 to NOB, Argentia, NFLD.
Perhaps in his case Officer Means Warrant Officer and not a commissioned Officer.
In May 1945 he was still serving on the Penetrate and was a Chief Bosun (T) service number 326728
Also on that muster list is another entry for him which says that he was detached from the US Navy 3297 Order of 28th April 1945 Comdt. 13th N.D. pend. ass. by BuPers. Auth CO Navy