When is it necessary to purify your DNA during cloning?

I cleaved a vector with two enzymes, after which I would like to blunt the ends and dephosphorylate before ligating to an insert. The insert was PCRed out from a different vector and then the ends were cleaved with an enzyme that creates blunt ends. I would like to reduce the purification steps to a minimal so that I can conserve the amount of DNA I have. Below is the process that I believe would be sufficient, please let me know if there are any additional purification steps that are required or if there are any I can skip:

Vector: Double digest -> gel purify -> Blunt the ends -> dephosphorylate -> ligate
(if I am using an alkaline phosphatase for the dephosphorylation I believe I can inactivate it and therefore skip the purification step before ligation?)

Insert: PCR -> gel purify -> restriction digest -> gel purify -> ligation