My guys have a hard time resisting a scooped and replennished litter box!
Maybe if you try that, then just hang out close so you can get the strip into the urine stream. Sometimes, especially if they pee a lot, there's a little "pond" on top of the litter you can dip the strip into. Grayson also used to pee out to the side of the box (I use Rubbermaid tubs now). If Boo does that, you can put the strip into the urine on the side of the box/tub. Initially he never peed when I was in the room. Once we started testing, he lost all vanity and I just held the ketone strip in the stream.
With high numbers, not enough insulin, and an infection, ketones can pop up in no time. It's REALLY important to test for them regularly, AND when there's a blip in kitty's numbers or any other change, to be especially focused on testing. If you catch it early you can avoid DKA. When Grayson had a ketone scare last year, I called the emergency room at NC State Vet School. They said if I brought him up there, it would be $3-4,000. Mind you, most of the cases they see, the cat hasn't eaten for 4 days, can't shoot, etc... G was just on the tip... and I was able to give him fluids and get more insulin into him. Fortunately, he was eating ravenously, so he had food on board. That's probably what kept him out of going DKA!
Do what you have to do to get the tests. For a while, I moved his litter box up to table height so I didn't have to bend over to catch him... strips were next to the box. That made it much easier!
Good luck!