I've used the puzzle blades on 1/8" plywood with no problem....Other than it takes a lot of time.
Even if you veer off of the line, who would ever know it? As long as the pieces fit you are OK.
Some people don't even use a "cutting pattern" at all, they just free hand the entire thing. Let it go where it may and it will be all right.
The thinner puzzle blades just let things fit together much better and will make tighter turns when cutting than the larger, thicker ones.