So you can go to the image, copy and paste it into your comment, and use it from your own instance. You won't have the emoji picker unless you have a hexbear account, but you can bookmark and hold on to your favorites.
if you're on hexbear.net all the comment boxes have an emoji button next to the other formatting options. You can scroll the pop-out box (go past the generic emojis). There's also a search-by-text, but for the most part you gotta get the name just right or it won't show.