Hi,
I did some tests on Safari with browserstack.com and I did see that sometimes, when I click on the menu icon to bring it out, it doesn't open and I have to click several times.
However, the browser's javascript console doesn't display any error when that happens.
I also can't check the javascript code on the page since you're using JCH Optimize and all the JS is compressed together, making it unreadable.
I can't say that it is or it is not a HikaShop issue at the time. However, seeing that the issue is in the menu system, it doesn't seem like it.
It's probably more of a javascript library conflict and using jquery easy is a good idea. But you need to make sure you deactivate JCH Optimize when you do your tests and configure jquery easy since otherwise, JCH Optimize will mess up the tests as long as its cache is not cleared each time, and even so, since it also concatenate jquery's code with the rest of the javascript, jquery easy might not be able to find jquery's code and properly handle it.
I would recommend to turn off JCH Optimize for now so that we can better understand the situation and that you can properly test jquery easy.