Hello
I haven’t been yet personally (better add it to my list!), but discussed it with @oshidori and they found a link to a Japanese site discussing the accessibility of the shrine. It is only in Japanese but you can put it into Google Translate to get the idea.
But, basically, if you park at the #1 Parking Area, it is paved and you can then access an elevator up to the main shrine via the Hall of Treasures (you don’t need to pay to enter if you just want to use the elevator). There is a wheelchair path leading to the main shrine with ramps etc. There are also two accessible toilets.
Unfortunately, the website report assumes you will be driving (or using a taxi)… how do you plan to go?
Here is the site:
https://ikiru-chikara.org/hakonejnzya/
Again, only in Japanese, but you can see in the maps that there are some accessible spots marked out.
https://hakonejinja.or.jp/hakone/keidai.html#link_01