The process of neatening up the Rhododendron is quite easy. I am right handed. With my left hand, I hold the wilted flower stem, just below the new growth nubs, (see the illustration). With my right hand I snap off the spent flower / stamen (seed pod), at the brown spot on the illustration. The process goes quite quickly, and the plant feels a bit sticky to me. The main thing is to not snap off the growth nubs. That is where new branches and next year’s flowers will come from.
The reason we always took off the wilted Rhododendron flowers was to made the plant look better, and it made it easier for the new growth to develop. The stamens/seed pod does get in the way, and as the flowers all fall off, you have those stamens turning a brownish color, which we always thought was unsightly.
So maybe this year, you might try neatening up your Rhododendron. The first few dead heads that you snap off, might be a bit scary to do. But after those few, you will be a pro at doing it. And, as for not snapping off the growth nubs, here and there I snap one off. But OH WELL, that is life. Happy Snapping!