I would suggest looking at TS menus before going and then when there asking for something to be made special using ingredients that are advertised as being available, especially with the salads. I've had great success at some of the higher end TS restaurants getting sautéed green veggies and wonderful salads. I'm not even sure asparagus was on the menu but the chef offered it to me and it was delicious. I've always gone in very open-minded and asked the chef if she/he has any suggestions for something that would be easier for them to prepare in the kitchen. More than once their eyes have lit up with the request of something healthy, fresh, and green and letting them be creative.
There are many low carb snacks that take up minimal space...moon cheese, nuts, salami or jerky. I have only found a couple items at WDW that are keto-friendly. Many resort QS locations have hard-boiled eggs to-go. Some QS will have basic to-go salads with iceberg lettuce. The resorts that have DVC will have a grocery section in the QS or gift shop and there is bulk packaged cheese, lunch meats, raw bacon, butter, etc...basically dirty keto. I prefer to order groceries from off-site and bring from home some higher-fat salad toppings like hemp hearts and pine nuts.