Any hotel best recommendation which can provide private tour for 5 of us to travel to Hengen shri...

Hi again

According to the official Sightseeing Association of Kawaguchiko and Hotel association, there're no hotels which provide private tours as far as they know.
But you can arrange your own tour guide wherever you stay.

And, one more important note is, there are A LOT of Shrine called "Sengen Shrine" especially around Mt.Fuji area, because this shrine's name came from and based on the mountain worship for Mt.Fuji.
The biggest Sengen Shrine is formally called ”Kitaguchi Hongu Fuji Sengen Shrine"(http://www.sengenjinja.jp/english/index.html) and there is an other Sengen Shrine in Oshino-Hakkai called "Shibokusa-Sengen Shrine".

I think this website will be a good help for you to find the places you wish to visit.
http://www.mt-fuji.gr.jp/english/

And also, you can arrange your private tour guide online from;
http://oshino.jp.e.nz.hp.transer.com/guide.php
I searched some tours or the guides around kawaguchiko and Fuji area, but I couldn't find any but this one.
I made a phone call to make sure if they can arrange the places as you wish, then they answered YES.
You can find a form where you can write down all your wishes.
As soon as they received your request, they will reply to you by email.
I recommend you to send your requests and find what and how would be the best for visiting the places you wish to before you come to Japan.

Hope this can be your help!