>is there a shortcode attribute available?
No.

Typically, you simply just do not upload an image , if you do not want to show it.
However, if you have assigned a product to 2 different categories and one is supposed to show the image and the other is not, your options would be to either use css (which would be the simplest way) or you will have to edit the loop template depending on category

first of all i would suggest having a look at the
faq:s
https://www.wp-pizza.com/topic/customising-the-css/
https://www.wp-pizza.com/topic/can-i-edit-the-templates/

generally, if you want to hide the images for your “desserts” category for example (adjust as required) it would be something like (not tested, but should work)

article.wppizza_menu-desserts > .wppizza-article-img{display:none}

(i assume you know what css is and how css declarations work)

you’ll find the loop template in “wppizza/templates/”
(depending on layout you are using you might have to edit either wppizza-loop.php, wppizza-loop-responsive.php, or wppizza-loop-grid.php)
I would however suggest you use css for this (see above) instead of messing around with those templates!