Hi,
I think you can do it with HikaShop using options:
demo.hikashop.com/index.php/en/hikashop/...ct-page/with-options
The options on that page are displayed as a dropdown. However, you can change the "Product selection method" setting of the HikaShop configuration to "Checkbox" and you'll get checkboxes instead of dropdowns.
So you'll need to create first a characteristic "option" with the choices you want to be available as values of the characterisitc.
Then, create an unpublished category and create a product in that category. In that product, add the characteristic and add the variants for the different values. Then, edit each variant to configure the price of the option, and in the "name" of the variant, enter the HTML of an img tag for the image of the option.
Finally, in your main product, add the option product in the "options" area and you'll get something quite close to what you have on your link.