I think you already answered your question. It would be a within-group, pre-post design. You could analyze the data using a repeated measure Ancova controlling for baseline stress. Hope this helps.

After looking at your question first thought of mine shed on "quazi experimental designs"

These are some of the articles that are available in Research Gate itself.

Years ago when I was just a student of Psychology I studied these in a book "Tests, Measurements and Research in Behavioural Sciences" A.K.Singh. There is a chapter on these designs. At present, I found a few of the articles in RG.

Article Selecting and Improving Quasi-Experimental Designs in Effect...

Chapter Experimental and quasi-experimental designs

Best wishes

In addition to what Cory Cobb said, most people would also recommend you counterbalance (i.e. assign randomly or quasi-randomly to each participant the order in which the two conditions are presented).