I wouldn't do that trip in 4 weeks. Not for a vacation
. Sure, it could be done, but you wouldn't get enough time in any area. There's soooo much to see, yet you'd just see it for a bit an have to move on.
And to keep to a schedule, you might have to spend a far amount of time sailing in conditions you otherwise might not want to.
We were in St. Lucia on our boat for 8 days in November. We went from St. Lucia down the the Tobago
Cays and back. Very doable in a week, but we could have easily spent 2 weeks without going any further, spending a couple of days in each location, doing more land exploration..etc. 3 weeks or more if we had hit all the other islands in that same area that we skipped.
If you really want to see if you'll enjoy it, try to put together an itinerary.