Hi,
The two stations near the museum are not connected, but both of them are close to the museum and are accessible.
Oedo Line doesn’t require a transfer, but you will need to walk to Shiodome Station (and the area is a bit confusing with overpasses and elevators in odd places).
JR will require a transfer, but you can leave from Shimbashi Station. Also, if you are using a JR Pass it will not cost you extra (Oedo Line will cost regular fare). Though it is less time on Google maps, be warned that transfers (particularly on JR) can take 15 minutes! So, it may be longer than planned/expected.
So, six of one, half-dozen of the other…
Hope this helps!