You could try emailing the guest house where you are staying on Male to ask them what day trips are possible.Edited: 28 July 2017, 09:01
There are any number of agencies in the Maldives who'll arrange this for you. You can contact your guesthouse, who'll be able to put you in touch with a tour company. You could also try https://secretparadise.mv/
I think you should be able to get to Vilingili by yourself by public ferry if you check the timetables.
We stayed overnight in a small hotel on Hulhumale and they had a brochure advertising trips so it is something that they are used to organising.
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