Pin headers that fit perf board that taper to DIP/SIP leg width
The phrase to search on is "DIP header". But I tried this myself and when I dug down, I found it surprisingly difficult to locate suitable products. Apparently, this is a niche product whose demand is fading in the past.

So, although we don't normally do product recommendations here, I'm going to offer the Mill-Max 350 series of single-row headers. Their 0.018" DIA round pins are much easier on IC sockets than the usual 0.025" square pins are. I've used them  myself when stacking boards directly to each other, and you can get them at Digi-Key, among other places.