Iqbal is one of three players dropped, while Watts is added to the squad
Scotland have dropped Qasim Sheikh, Moneeb Iqbal and Calum MacLeod for the ICC World Twenty20 after a disappointing World Cup campaign.
The Scots missed out on qualification for the finals in South Africa.
And Fraser Watts, Gordon Drummond, Glenn Rogers and Richie Berrington have been added to the squad for the June competition in England.
Gordon Goudie, missing through injury, is the other absentee from the side that disappointed in South Africa.
Chairman of selectors Iain Kennedy said: "The selectors and the captain spent a considerable amount of time discussing the squad as we must balance the longer-term development of the team alongside the need to perform well on the world stage in the shortest form of the game.
"We believe that Fraser and Richie will give us new batting options, as well as contributing significantly in the field, whilst Rogers and Drummond will offer variety to our attack.
We have made some positive steps forward in the last couple of weeks
Scotland captain Gavin Hamilton
"There were a number of very close decisions made about the personnel required for T20 and we are sure the selected squad will perform well against the best sides in the world."
Eleven of the 15 players represented Scotland during the inaugural World Twenty20 in South Africa in 2007.
The Scots face New Zealand on 6 June and South Africa the following day, both at The Oval, in their initial Group D games.
Warm-up games are scheduled against England at Trent Bridge on 2 June and the Netherlands at The Oval the following day.
Gavin Hamilton had already been named as the new captain, but former skipper Ryan Watson retains his place in the squad.
Hamilton said: "This event will be a huge test for us all, playing some fantastic sides on the biggest stage cricket can offer.
"We have made some positive steps forward in the last couple of weeks and the full squad is looking forward enormously to testing ourselves against the world's best.
"It was pleasing that we had some difficult decisions to make as this shows we have a number of players capable of playing at this level."
Scotland squad: Gavin Hamilton (captain), Richie Berrington, John Blain, Kyle Coetzer, Gordon Drummond, Majid Haq, Neil McCallum, Navdeep Poonia, Dewald Nel, Glenn Rogers, Colin Smith, Jan Stander, Fraser Watts, Ryan Watson and Craig Wright.
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