No answer possible without knowing further details.
1. what it your citizenship? what passport do you have?
2. which caribbean country do you plan to visit as tourist?

Some Caribbean countries like the Bahamas or Jamaica allow most Commonwealth citizens visa free travel. The same applies for some British Overseas territories.

If you do not add additional details you may also check your visa requirements on ..
< http://www.klm.com/travel/ch_en/travel_information/travel_planning/travel_clinic/visaform.htm >

Edit: (based on additional details)

You will need a visa in advance to travel to Australia, Brazil and Japan. Switzerland has joined the Schengen agreement and requires a visa from UK residents since December 2008, too. You may get a visa on arrival for Egypt which is free of charge and authorizes a stay of 15 days if you enter Egypt through Sharm El Sheik, Saint Catherine or Taba airport and remain in South Sinai tourist resorts and do not continue to any other city in Egypt:
Your Bangladesh passport enables a visa free entry as tourist to the Bahamas, Barbados, Bermuda, Dominica, Grenada, Haiti, Jamaica, Montserrat, Saint Kitts & Nevis, Saint Vincent and the Grenadines, Turks & Caicos Islands.
A tourist card can be obtained for Cuba by booking the travel through an authorized travel agency.
A British residence permit enables visa free entry to Aruba and the Cayman Islands and to get a visa on arrival for the Dominican Republic for a fee of US$10.