You can substitute all sorts of things if you don't have cooked crab on hand. In order of preference, I'd choose crawfish, lobster, shrimp, octopus or regular fish. This is best eaten soon after it's made, although it will keep a day or so in the fridge.
Gently mix the crab with the lime juice. Mince the onion first and fold that in before you chop the other vegetables; this helps take the sting out of the raw onion.
Fold in the remaining ingredients and serve on the tostadas. It is important to not let them sit around, or the tostadas will get soggy.
NOTE: If you are making your own tostadas, fry them in 350°F oil until they mostly stop bubbling, about 2 minutes. Drain on paper towels and salt lightly when they come out.