There are a couple of things that I think that you can do:

Learn your lowest shutter speed: At 24mm, I would have expected you to be able to hand hold 1/25 and especially 1/60. Now, that might be too low and your subject might move, causing motion blur, but you shouldn't be getting camera shake at those speeds at that focal length. You should practice steadiness and proper grip on the camera.

Pay Attention and Adjust on the Fly: Just because you're using Av doesn't mean you can treat your camera like a point and shoot. The shutter speed that the camera will use is displayed in the viewfinder. You should be glancing at this at minimum every time the lighting changes to ensure shutter speeds that you can handle.

A quick and dirty way to change things is to underexpose the shot. If you notice that the shutter wants to be 1/25 and you know you can't hold anything less than 1/50 then it's a quick adjustment to knock the exposure compensation to -1, which will let the camera know to go to 1/50. Yes, you'll have to clean this up in post, but, if timing is of the essence and you're already at your minimum Av...

Conversely, if you're not at your minimum Av but have selected a favorite for sharpness or DoF, then ask yourself if you can open up a stop for this one shot.

Add Light: If you are in a situation where you are wide open, at your max ISO, and the shutter speeds are stills too slow, then you have to add light. Start learning about flash.