In WWII the USN used "black oil" or "bunker fuel", officially called Bunker C or No. 6 (and by the Brits/CW FFO).  As a residual oil black oil was viscous and rather sludgy, meaning it had to be heated before it could be pumped; no oiler built since the advent of DFM* would have the gear installed to do that.  DFM and bunker also require very different nozzles in the burners. And AVGAS required very special handling spaces and gear, which Success doesn't have.  OTOH, in WWII it was handled by gasoline tankers, AOGs not AOs, so Success would be off the hook when it came to supporting carrier aircraft.

You have another problem- no WWII ship would have receiving stations equipped to take a modern probe hose-connector; they'd have to jury-rig the connection somehow.

*Distillate Fuel Marine or Diesel Fuel Marine

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"He that will doe no worke shal not eate. The labours of thirtie or fortie honest and industrious men shall not be consumed to maintaine a hundred and fiftie idle loyterers." --Capt. John Smith, Jamestown