Hi,
No, there is no option to select another menu for the links of the current menu.
Because normally, you don't want to switch from one menu item to another for the links of the pages of one menu.
The canonical URL is indeed a solution here, and that's the only solution I can see available, unless you change the code of the views in HikaShop.
For example, in the file "listing_img_title" of the view "product", you can see that the link is constructed like that:
$link = hikashop_contentLink('product&task=show&cid='.$this->row->product_id.'&name='.$this->row->alias.$this->itemid.$this->category_pathway,$this->row);
So what you can do is change $this->itemid before that line to set the Itemid parameter yourself.
For example, like that:
$this->itemid = '&Itemid=18';
where 18 is the id of your menu item.
And all the links of all the menu items and modules using the layout "image and title" will use that menu item automatically unless they have a canonical URL and you turned on the "force canonical URLs on listings" setting.