IMHO....either the ski poles or the trekking poles will help.

The ski poles...you could find cheap at a garage sale.
The trekking poles...

Ok...I have trekking poles...(remains of a past life)

anyhoo....I have tips I can switch out. I have some that converts them into a ski pole and the rubber tips (covering the every so sharp---poke the bear in the eye-- carbide tip).

anyhoo...with the rubber tips on...now I use them for canes.

I would walk my quarter mile to work...but by the time I get all the raingear on and it gets soaking wet, then take it off and your shoes are soaked. It would be time for lunch!

I say go for it!