I am not able to update whatsapp due to download with different account

You can't. If the chats are backed up to a different iCloud account, you cannot get them back.

It should still show some recent chats though when you set it up.

For further help, contact Facebook / Meta as Whatsapp belongs to them.

click here ➜ https://faq.whatsapp.com/209942271778103/?cms_platform=iphone

I don't know how Whatsapp works. You should ask this on a forum for WhatsApp. Some apps store data specific to an Apple ID, so if you download with a different ID you lose all the data. Others store data on the app's site and if you log in with them it should reappear.