You would like to convert all icons to SVGs right? Do you have the svg version available or you want them converted also? It should be possible by changing in the code. Here is a thread of how to add logo https://community.shopify.com/c/Shopify-Design/add-svg-LOGO/td-p/499871
The gif within svg works as long as it is inline embedded not referenced as a file outside.
check this https://codepen.io/bjango/pen/dfvmB