The Scots stunned France with a 20-16 win in last weekend's opener and Scott Lawson is the only change from that winning side.
The 24-year-old Glasgow Warriors hooker will make his first start in the tournament and he replaces Dougie Hall of Edinburgh Gunners, who is omitted from the 22.
Border Reivers' Ross Ford is rewarded for his consistent displays in the Celtic League with a place on the bench.
Hadden said: "The decision at hooker was an incredibly difficult one to make.
"I've said all along that we have three top quality performers in that position.
"Now is the opportunity for the other two to show what they can do.
"It's unfair to suggest that Dougie is carrying the can for any problems in our lineout last weekend.
"We challenged ourselves in that area by deciding to go for full lineouts to enhance our driving maul and full lineouts are the easiest to defend against."
Marcus Di Rollo is continuing to make progress from his sore hamstring from the French game.
Hadden added: "We will be monitoring him closely this week and obviously we will be considering other options.
"Ben MacDougall and Graeme Morrison will both be with us in training."
Scotland team to play Wales at the Millennium Stadium, Cardiff, on Sunday, February 12:
H Southwell (Edinburgh Gunners); C Paterson (Edinburgh Gunners), M Di Rollo (Edinburgh Gunners), A Henderson (Glasgow Warriors), S Lamont (Northampton Saints); D Parks (Glasgow Warriors), M Blair (Edinburgh Gunners); G Kerr (Leeds Tykes), S Lawson (Glasgow Warriors), B Douglas (Border Reivers), A Kellock (Edinburgh Gunners), S Murray (Edinburgh Gunners), J White, capt (Sale Sharks), S Taylor (Edinburgh Gunners), A Hogg (Edinburgh Gunners).
Substitutes: R Ford (Border Reivers), C Smith (Edinburgh Gunners), S MacLeod (Border Reivers), J Petrie (Glasgow Warriors), C Cusiter (Border Reivers), G Ross (Leeds Tykes), S Webster (Edinburgh Gunners).