What's the verb for making that "pffft" sound?

I don't believe there is an actual verb that describes this particular action. However, I can suggest some alternative words that might convey the sentiment expressed by the noise.

I think to scoff is a good option here. It makes me think of someone making a sarcastic snort, which is pretty much what "Pfft" is in this context.

You might also consider to sneer, although this seems less like a sarcastic laugh and more like a nasty face to me.

And you could always use an adverb: "That worked well," he barked scornfully.

If you ask me, "pfft" is what he/she says, and it seems to convey the meaning directly to anyone who understands that sound. I'd be inclined to consider "Pfft" a word, on that basis. So, if it's a word, and your character says it, why not include it in the dialogue?

Otherwise, you're left describing part of that the character says, then including the rest of the dialogue

John puffed, then said "That worked well, we not only have the entire police force but also the entire mafia chasing us"

Or else implying that she may have said something like that, or maybe not

"That worked well, we not only have the entire police force but also the entire mafia chasing us," scoffed Kitḫ.

The second sentence works fine, and isn't clumsy, or wrong, but if you intend to convey that your character said "pfft" then I think you should write it.