I’m glad you realize you won’t be doing much designing in Mechanical Engineering. I didn’t before I went into it but, like you, I’m not sure if I would have been happy in pure ID without the physics, calculus, etc.
What I would suggest is find out which one is most important to you, then do the other in your spare time. Once I found out I wanted to do design as well, I found some students in ID and asked them what their favourite textbooks were, then bought a few and read them front to back, working through the exercises as well. There’s a thread on this board that has some great design books listed, and if you decide to go into ID I’d be happy to recommend some engineering text books.
Depending on where you go, there may also be opportunities to take classes in the other discipline, though the elective slots in engineering are virtually non-existent (I got one elective in 4.5 years).