Do you know what sort of light you have ?
With live plants, you'll need to have the light on long enough each day for them, however, if you have good hides and plant wisely you can create a lot of "shade".
I have a normal output T8 fluorescent bulb and while it looks really bright, I will still see my axolotl moving around when it's on - she usually sticks to the shady parts of the tank, and is less active than when it's off, so I do have the light timer set so that the light can turn on while I'm at work.
You'll just need to have plants that will do well with your lighting and the cold water of the tank - and ones that are aquarium safe. I know java fern, java moss, and hornwort are popular. I have both of the former and other types, I'm new to plants myself, so I picked ones that would tolerate the light level and temperature and that looked good and "functional" - I like watching my axolotl climb and perch in the plants, so I picked ones that seemed to be well-suited for that.
Also, axolotls tend to swim into / through plants, so more delicate ones might be uprooted on a regular basis, especially with sand substrate. Some can be anchored with/to rocks or on driftwood/bogwood.
I'm not sure about floating ones, I haven't tried any yet, but they'd certainly provide some shade.