Hi all....I'm a PT student, and know plenty about DVT (as I just spent 12 weeks working with people who have them in a hospital).
As OP said, sitting for a long time (such as in a wheelchair OR
ECV) is NOT good for your legs (it's called the "dependent" position) where legs are hanging down. That will contribute to a DVT forming. A thing to watch for with your legs is 1) a fluid buildup. If you press on your lower leg (below your knee) and it makes an indent that takes a long time to go back to normal, then you have lots of fluid in there. 2) red/hard skin below the knee. Again...another sign that your fluid carrying system isn't working right. 3) a deep ache of pain. If the pain feels like it is way deep in your leg and is bothering you, this is NOT good either.
Monitor all of these symptoms closely, and GET MEDICAL ATTENTION! If have any/all of these, and experience shortness of breath or a really hard time breathing....GET HELP! This may be a pulmonary embolism where the clot breaks free from your leg, moves through your blood, and travels to your lungs.
My suggestion as a medical professional would be to wear the compression stocking suggested by your MD. They are nothing to be ashamed of, and will only benefit YOU (who cares what others think)! Second, IF walking is too much for you, take time to sit (enjoy the Topiaries) and do ankle pumps (as if you stepping and letting up on the gas pedal) throughout the day. That is the #1 thing I tell my patients. You can also straighten your knee out while you are sitting (so almost like you are doing kicks from the knee). Both of these things will help your body pump the fluid back up to where it belongs.
DVT is not something you will know you have. It will have to be diagnosed medically at the hospital, usually with a venous Doppler.
Please keep all these things in mind, and have a great time on the trip!