Hi jansparkle -
Welcome to My Swiss Alps. You are not the only one who likes Wengen:
It is my favorite town in the region, as well.
My suggestion is that you should close your eyes, or, go to Grindelwald and use the cableway upwards with smaller cars. Of course, that might be worse...not sure. If you can ride the cableways up to Mürren, this one should not be all that much harder. (Easy for me to say....;-) )
You can go in the "wrong" direction, as you suggest, but , then, you still have to ride the cableways back down...unless you turn around and walk back the "right" way. Or take a very long downhill walk to Wengen or Grindelwald ( or, Alpiglen, perhaps) on steep trails.
If you go from Kleine Scheidegg to Männlichen you have a modestly uphill walk...about 180 meters elevation change, at 2000 + meters elevation, in about 3 or 4 km. Plenty of people walk it in that direction. It does not have the nickname "The Grannies' Trail" for no reason. You will see Swiss grannies with their hiking boots going uphill at a brisk pace. Tourists...not so brisk. But, it is easier to go downhill at that elevation, unless you are accustomed to the "thin" air.
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However, what you miss completely if you walk away from the Eiger, even if you pause every few seconds and turn around to look, at the cost of time and a sore neck, is the psychological effect of having the Eiger approach you and tower over you as you walk toward it. You really want to have it in view constantly as you approach it.
It is compelling.
The attached image shows the trail as it nears Kleine Scheidegg, and a magnified crop from it, showing hikers that are only visible as specks in the full image.. It tells you just how overwhelming the Eiger is. (Yes, I know the image is grainy. It was taken a few years ago with a medium called "film." ;-)