Painting the Outside of a Metal Lamp Shade?

I think the spray paint will bleed. You might be better off using a brush.

There is a risk of bleed either way. Some folks have good luck with taping plastic bags (like black plastic garbage bags) to the inside. My friend's late mother used to make this a two person job where the second person kept a hand on the plastic (like a small section at a time) while the other person spray painted. This really should be done outside and with both people using eye and face protection.

I'm not sure it is clear what type of shade you have.
By perforated do you mean there are 'holes' that you can see through to the inside brass lining?

If this is the case, is the top layer and the lining separated at the bottom?
If so you may be able to use something like parchment paper (baker's paper) and slide it between the layers and tape it to the inside of the lining.
I have even used wax paper for similar projects but I do not think this would work here.
If you are very proficient with spray painting it might work but you may have better control of amount of paint that goes into the holes if you used a small brush and took your time.

Whatever the case, try to do this in a protected outside area (no hot sun and no wind) and have plenty of paper/cloths down on work space to save on cleanup and lots of clean 'wiping' cloths.

If the perforations are small, you could try to fill them with hot glue and once you have spray painted the outside you could push out the hot glue fills from the perforations.