Safe use of LASER LED

my quest for entertaining of our can continues. I would like to use a LASER pointer so the cat chases it - but I am afraid about (eye) damage of someone or the cat. I have an old dead laptop and I want to dissect LASER from its CD/DVD reader but I know it is dangerously powerful. Wiki says <1mW of LASER light never caused documented damage and ~5mW causes damage very rarely and only temporal and only if you stare into the light for longer period of time.
So I wanted to use the LASER with current limiting resistor. As far as I know LASER LED behaves just as a common LED with voltage drop around 2V (depending on color). With 5V source and 10k resistor I should have around 0,6 mW LASER and be well in safe area (hopefully even for a cat’s eye). Still I would like to ask if someone sees a catch I have overlooked in this setup.

When you drop the laser power to 0.6mW is that optical power or power drawn from the power supply ? <1mW refers to the laser optical output power.

I meant power drawn from supply. I thought efficiency of LASER is similar to normal LED, at least 50%.

I don't like it.
Your 10k limiting resistor does help but is not enough to make it truly safe for cats. I don't know the eye safety limits for a nocturnal predator with big round eyes but it probably is more sensitive than for humans. The issue is not really "too much light" but "all of it at a very focussed point on the retina". By going to an LED instead, you keep the brilliant pure colour and all optical fast movement, but make it safer than a laser because the LED cannot be focussed to a point like a DVD laser. They often focus to a square, which the cat will chase just the same. So for the eye safety of the cat, spend a $ and get a ten-pack of bog standard LED's. You can even choose your favourite colour for it.

Some time ago I managed to get the red laser from DVD reader working and found the problem. The laser is very wide compared to laser pointers - I guess over 2 mm diameter. For comparable brightness much higher power is needed. So with safe power levels the "dot" is nearly invisible. For anyone thinking about the same: it is impossible to do safe laser pointer from DVD laser unless you can somehow make the beam much narrower. Maybe just moving the LED closer to its lens would do the trick but it needs too much too precise work for me.

AFAIK lasers from DVD (burners) are NOT safe to play with.