I'll assume that the two words have nothing in common, so: a) To swing something= as a verb, it means an action similar to suspending an item and moving it in a direction while holding from one end (thats the best I can think of really. Better seen than described in words). b) Catering menu = Well… I think its a set menu where you can order food from a catering company. Going to swing a catering menu at someone?

Swing could be physical, like moving back and forth or side to side, like a pendulum on a clock. Without much context, "to swing" something could also be "to arrange or to manage to do something". For example, my friends invite me to go to the movies tonight, but I'm working late. I could respond: "I'll try to leave by 8:00, but I'm not sure I can swing it, so don't wait for me if I'm not there by 8:30." I suspect that a catering menu is a menu/list of foods that a catering service offers. A catering service provides food for large quantities of people. For example, in a conference, there is usually a catering service that provides the coffee, beverages, donuts, etc. A wedding reception is also a catered event, where the caterer provides the meal for all the guests. In this sense, a catering menu would be the foods or meals that they offer and can provide to serve a large quantity of people.