The skin permeation profile (particularly the lateral diffusion coefficient) of a diclofenac (DK) transdermal patch, and percutaneous absorption in general, are in question here. I include the medical terms, mostly because it may help finding further reading beyond what I suggest.
An approachable introduction to percutaneous absorption is a review written by Dr. Paul Brisson (it was in fact, used a source text in my schooling).
Lateral diffusion, how any drug spreads out from the application site as opposed to down through the skin, varies on how the patch is actually made. This is often measured as cm2/h, as the diffusion happens over time. It should be noted that even with the constant application of the patch, you are going to get reduced diffusion based on concentrations gradients which roughly follow Flick's laws of diffusion.
A standard salt gel formulation of DK (which is a good baseline, as any modifications will be at best 100x change in ether direction) has a lateral diffusion coefficient of
9.65x10-9 cm2/h, and a rough saturation time of about 3 hours. Even if we assume 10 hours of diffusion, and a 100X increase in the coefficient (
9.65x10-7), that still only gives us
9.65x10-7 cm2 lateral diffusion. Let's round that off to an even 97 square nanometers.
That's smaller than the cross sectional area of many viral particles. So you are quite right, a patch is most directly treating the area that it is directly on top of. But this ignores another factor in patch dosing, which is that the drug is transferred to the plasma (blood), and then distributed systemically throughout the body. Thus a significant portion of the dose that a prescribing physician is intending you to recieve might be through delivery from the blood.
So yes, you can sometimes cut a patch to deliver the drug better to a local area, but you should first check with your medical professional to be sure that the type of patch you are using can in fact be cut and still effective (some the nanogel suspensions can't be).