Firstly,
Customs in Cruz Bay is, or was up to yesterday closed and check/ins have to be done in Red Hook, St Thomas, close to American Yacht Harbor or by Havensight in Charlotte Amalie.
Secondly, if on a private
boat your
captain will be handling check ins but all passengers must be there.
Personally I have not been required to check out myself (UK national) or my boat (private, UK reg) on leaving USVI shores, so always had entry but not exit stamps if I went to the BVIs. Other islands do require exit papers.
Phone landlines are still mostly not working after the hurricanes in September, therefore there have been problems also with online systems here.
Visa Waiver SHOULD
work for you, but that can sometimes depend on the attitude of the Official on the day.
Good luck and I hope you enjoy your visit!!