Former Colchester boss Williams took over from Brian Flynn last summer, and oversaw two defeats as Wales came up short in their bid to reach this summer's finals in Israel.
With several of the older members of his last squad no longer eligible for selection, Williams has included seven uncapped players in his squad for the friendly in Llanelli.
And Williams is looking forward to having a new group to mould.
He said: "We have a new group and in many ways this is a clean slate for us.
"I don't want to single out any individuals but I am happy with the group we have got and I am looking forward to working with them.
"We are excited about playing Iceland, as we should be every time we represent Wales.
"We will be looking to be solid at the back, you need to have a solid foundation so that is what we want to see.
"With the ball we want to be sharp in attack, to look to transfer the ball quickly and accurately, and if we do those things hopefully we will have a good performance."
Wales' will face a huge hurdle in their campaign to reach the 2015 finals after being drawn alongside Stuart Pearce's England side, as well as Finland, Lithuania, Moldova and San Marino.
Williams said: "The important thing is we were drawn as second seeds in that group, and we want to reflect that.
"A lot of people will focus on the England games, but we have to do our jobs properly everytime we pull on the red shirt.
"But obviously the England games will be great in helping some of the guys develop as there will be a lot of spotlight on those encounters."