Scratch

I made up a rather crude way to do it, which uses two sprites, one for each costume. Here's my project. 

I'm not sure how scimonster's works but using two sprites I've gotten a similar effect working. What you do is that you put a sprite with the second costume you are changing to under the first sprite.

The second sprite has this:

when gf clicked
set [ghost effect v] to [100]

Which effectively hides it from view. You can also put a hide block after the set ghost part to stop color sensing from being affected by it.

The first sprite should have the opposite in it.

when gf clicked
set [ghost effect v] to [0]

Now on your screen one sprite is visible and one isn't.

For the transition you want this in the first sprite after the above blocks:

repeat [10]
change [ghost v] effect by [-10]
wait [0.05] secs
end

For the second sprite you want this:

repeat [10]
change [ghost v] effect by [10]
wait [0.05] secs
end

And that's it. You can change the repeat and amount ghost effects changes by but when multiplied together they should equal 100 (e.g. 10 * 10 = 100).

Obviously you don't need to use the green flag clicked bit and that could instead be a key press or something.

I'll upload a version in a moment so that you can see how this way would look like.