In many cases, the shafts for wedges tend to be less stiff than the irons. Pros generally play XS in their irons and S in their wedges. Their weights tend to be a little less in their wedges due to the lighter flex (but only a few grams usually). But most wedges have a higher swing weight than the irons. Where most irons come standard round a D2 swing weight, wedges will vary from D3 to D4 in their standard swing weight to allow the higher head weight to add it’s own momentum into a partial swing or to get through sand with less effort.
Since my GW is my last full swing club, I generally build it with the same shaft and swing weight as my irons. But my SW and LW tend to have that D3 and D4 swing weights, regardless of shaft.
Most OEM’s use a Dynamic Gold S200 (stiff) shaft as their standard shaft. But if you’re building your own, you can do whatever you want as long as it feels right for you and you play well with them.