1st week of May should be fine. There are few things to take into account. Expect cruise such as Makruzz and Coastal Cruise to operate. As of now, the schedule of the sail is not yet out. However, we expect the cruise to not operate as usual.
Government Ferry will be operational to commute between islands.
You may expect rain during your visit, not heavy though. The island has a tropical climate and we expect rains all throughout the year. Even in December. As a suggestion we recommend you to move to Havelock/Neil Island as early as possible and return back to Port Blair a day or 2 early. The reason we say this is because, even if the weather goes bad then also you will have enough time to return back to Port Blair to take your departure flight. This is a general suggestion we give to travelers.
Originally asked to us at https://www.quora.com/Is-it-a-good-time-to-visit-Andaman-in-the-1st-week-of-May?share=1