If it's helpful to think of this poem as the "Magic School Bus: Journey to the Soul," go right ahead and set this baby inside some standard-issue human body with the soul dishing up its insights from the physiological depths. Just remember to push aside those "chains/ Of nerves, and arteries, and veins" (7-8) so you can actually see what's going on.
But Marvell probably pictured his poem in some kind of abstract space, as a philosophical exercise rather than a conversation happening inside the body or brain. After all, we're already going along with his image of a soul with a voice box. Why not go whole-hog and picture soul and body sitting down together at a cozy philosophical tea table? Scones, anyone?