Getting rid of the urea IMHO is the major issue (otherwise, you just could adjust pH or dilute into your experiment buffer). If this does not work, a buffer exchange into your pulldown buffer (or PBS or similar) using gel filtration on Sephadex G-25 (e.g. NAP-10 or PD-10 columns) should do the trick.

Urea should be removed slowly, otherwise the protein will not refold properly or not at all. Unfortunately this is not a simple task and most of the time the refolding buffer is critical. Moreover, everything depends on your protein. There is no single recipe. On column refolding is also an option, urea must still be eliminated slowly.

The His tag binds to the metal at neutral to slightly basic pH (pH 7.5–8 is typical) and the protein can be eluted by lowering the pH to 4–5, stripping the metal from the polymeric support with high concentrations of ethylenediaminetetraacetic acid (EDTA) or, most commonly, by competition with imidazole. Try to use IMAC resin and different elution strategy otherwise you may use centrifugal ultrafiltration such as amicon vivaspin for buffer exchange and ph adjustment...Renaturation is critical as the authors indicated and scrambled refolded states can be observed after urea removal resulting low activity protein...take a look at the thermo refolding kits if they suit with your target protein.