Hey Jonas,
making the shopping cart icon disappear on menu toggle would require re-writing the jQuery script that governs the behaviour of the mobile menu, yet you can relatively easily re-align the icon relative to the menu “sandwitch” icon by using some extra CSS (you can add it into the “Style: Add Custom CSS” tab of the Theme Options panel):
@media only screen and (max-width: 767px) { #wc-wrap { margin-top: -46px !important; } }
Sincerely,
Andrii / Satori Studio