Hi, 

By using fields_view_get() function, you can hide the menu based on the condition.

class StockPicking(models.Model):
    
    _inherit = 'stock.picking'

    @api.model
    def fields_view_get(self, view_id=None, view_type='form', toolbar=False,
                        submenu=False):
        res = super(StockPicking, self).fields_view_get(
            view_id=view_id, view_type=view_type, toolbar=toolbar,
            submenu=submenu)
        #
        #
        #Add your condition
        #
        if ((view_type in ['tree', 'form']) and
                res.get('toolbar') and res['toolbar'].get('print')):
            res['toolbar'].get('print', []).clear()
        return res

You can hide your specific menu from the toolbar by adding the appropriate condition

Hope it helps.