Interpolation/approximation of quarterly data into weekly data

After reviewing the paper on tempdisagge, I think you should take advantage of it. The denton-cholette algorithm is only one of available methods, with chow-lin-maxlog as the default.

Without a reproducible example, called a reprex and a notion of the domain, it's hard to give specific advice on how best to tune the methods in the package to your situation. However, a time series specific approach is more likely to give you better results than simple approaches, such as approxfun{stats} based on simple linear approximation.