These treatments can swiftly help patients be on their way to a more active life.
These treatments can help patients swiftly be on their way to a more active life.
I would use the first: "These treatments can swiftly help patients be on their way to a more active life."
Swiftly is an adverb, and the difference between the two is what is being modified. In the first sentence, the treatments help swiftly. In the second sentence the patient is swiftly on their way (swiftly modifies "be on their way").
I'm assuming you are speaking to promote the treatment, so the first sentence more directly incorporates the idea of speedy action by the treatment. The effect of the treatment is speedy, rather than a treatment that results in a speedy patient.
That's a picky analysis. Realistically, the two sentences are very close in the image they create.