Cache Issue with CURCY

I am running a Woocommerce website using LSCache and Cloudflare.
My CURCY plugin is using the COOKIE option with the Override by AJAX. These options is working well with the changing currency or the automatic currency by country.
But I found that my website has not been cached for the first visitor every time. It causes the slow loading speed and high TTFB.
If I change to use SESSION instead of COOKIE, my website is cached very well, and the load speed improves very much. But the problem is that if I change the currency manually on the product page, the price of the product still remains unchanged, while the price of products in the sidebar or related products section changes.
Do you have any ideas to resolve this issue?