Weld shape & keep cut lines?

Hi,
Is there a way I can weld or mesh the offset around my font, with my arch shape? I want those yellow lines to be cut lines … but when I select them and weld, the offset lines around my font just disappear. I really want to have my laser cut around the font… but also for it to be welded to the arch shape and “hold together” for a cut like the other pic.