There are two cold blue products I've used a number of the times in the past with good results. Oxpho Blue and Blue Wonder. Either one should do a decent job.

Have seen an Oxpho blue job done by a gunsmith. Have to think the guy dipped the barreled action in Oxpho. Owner of the barreled action also owned a small gun store. He too was stunned by how well the Oxpho looked.

As to Blue Wonder, prep for it is more tedious, but if I want the best looking cold blue job on a rifle, I'll use it. Recall day, I took a Ruger rifle back to a gunsmith a week or so after he'd put a chrome-molly barrel on it. I'd used Blue Wonder on the barrel after I'd picked up the rifle from the gunsmith. So happens, the gunsmith is outside when I arrived with the finished rifle and I show it to him. It's a bright sunny day and he's holding the rifle. Has a puzzled look on his face...asks me if the barrel was already blued when he installed it. The gunsmith was on the elderly side of life....I chuckled, saying, no you're not getting absent minded. I used Blue Wonder on the barrel. He smiled, commenting that Blue Wonder was good stuff. He used it himself.