Full-back Tom Jordan and hooker George Turner drop to the bench, while Jack Dempsey, Jamie Dobie and Jamie Ritchie miss out after being ruled out earlier this week.
The Scots opened with a loss in Italy before a convincing win over England.
Williamson came off the bench in both while Cherry and Fagerson also came on as replacements in the Calcutta Cup.
“I’ve enjoyed being in Spain this week with the players, it’s been great, we came here after a win and it’s been a good training week,” said Townsend. “Vitamin D helps with the soul.
“We want to show our fitness and conditioning in what will be a tough atmosphere and a tough game.
“You’re only as good as your next game and that’s what we look forward to. Our players are keen to go again.”
Townsend expects Wales, whose head coach Steve Tandy previously worked with Scotland as defence coach, to be “highly motivated” after defeats by England and France.
“They will have taken learnings from those defeats,” said Townsend. “They played very tough teams. They will be highly motivated and play with a lot of passion.
“The atmosphere is always one of the noisiest in the championship and I’m sure they will be playing their best rugby again. That’s the challenge we are preparing for.
“The plan is to play our game. We’ve got to adjust our game to what’s working. We can be physical, move the ball to width and also use our kicking game effectively. We also have to work out what the opposition are doing – we have to deal with their threats.
“Coaches don’t go up against each other. It’s the players. It will be great to see [Steve Tandy] after the game. We’ve been sharing messages – not many this week – but in the first couple of games.
“We think very fondly of Steve, he spent a long time with us and has been a big influence on our players. I’m sure after the game we can have a few beers.”
