Can Display Suite render content without my theme around it?
aDisplay suite should allow you to modify the output for the fields and even choose some layouts but AFAIK it won't let you completely omit the site theme (i.e. create a page without header or footer).

You can use js/ajax to grab just the portion of the page you want to appear in the modal pop-up so that it doesn't pull in the header/footer. Depending on the JS library(ies) you are using this could be easy or challenging.