Custom currency switch

I’m trying to build a custom switch between two currencies (USD and EUR). USD is the default currency.

I’ve built the custom switch as a toggle switch which on toggle will set the value of Cookie: wmc_current_currency

So for example, switching to EUR will make the value of wmc_current_currency = EUR. Then refresh the page.

This however does not work. It sets the cookie and I can see the value becomes EUR. But the page does not reflect that.

If I visit ?wmc-currency=EUR, then it works.

I want to avoid using the query string as it takes a lot longer to load the page and I want to avoid showing a query string to my visitors.

As mentioned in https://codecanyon.net/item/woocommerce-multi-currency/20948446/comments?page=29&filter=all#comment_26578310, the issue is related to my site using caching.

I’m using W3 Total Cache and when I deactive the plugin, the switch works. So it is definitely a correct assumption.
Question though, is there any way of working around the cache issue?