I suggest to you to evaluate the Pipe cloning approach which let you free from restriction enzimes.
you need to perform an insert per from your parental vector and a vector pcr of your destination vector with primers containing overlapping flags, digest the pcr with dpni to remove templates and transform the mix in thermo mach1 competent cells.
its a nice methods
you can find more details about it and primer design in my blog ProteoCool
Overlapping Extension PCR is one approach to avoid using the existing restriction sites. Or you can incorporate flanking sites in the insert by PCR whoch correspond to the target vector. It all depends on your available resources and financial situation.
Yes, the overlapping extension PCR as recommended by Prof. Thomas could be performed. Furthermore Manuele's approach of using the pipe cloning technique sounds a possible alternative too.