I'm not sure what you mean about the spline design matrix (I don't have Wood's book in front of me), but I imagine that you could get anything design matrix related from that code directly or with small modifications. AFAIK there isn't any code in there to compute the penalty matrix at all, though.
Your best bet is probably to make your own implementation of the splines, while stealing anything useful from that file in the process?
You might want to ping github user @broessli, who wrote that file. Their motivation was just to be able to take models that were fit using mgcv in R and then do predictions in python, so they didn't need penalty matrices. But they might be interested in helping or have some advice for your project as well.
Good luck!
-n