I would at least saw cut the column section, so I got a good true, square bearing end. But, look at the mill tolerances for W shapes and you’ll see that the beam flange can screw this up. This detail requires some special attention to fit-up out in the fab. shop, maybe even straightening the flg. a bit for good bearing and fit-up. We milled large/heavy column sections (larger W14's, heavy built-up sections, etc.), I don’t remember off the top of my head what the size or design criteria was for requiring milling. We finally got a larger saw on our beam line (about a 6-7' dia. circular blade, with machine tool teeth) which operated much like a milling tool. Then we didn’t have to mill rolled shapes any longer.
Slick’s first approach seems a little busy, I’d opt for his second solution. And, I’d mill order the column long enough so that while I had it on the beam line, I’d cut the col. to length and then make a second cut which would fit from flg. to flg. on the beam. I’d rip this short piece to make my own WT’s. I’d clip its web for the radius at the flg./web on the beam. If the col. has a ‘d dim.’ greater than the beam ‘bf dim.’, I’d cope the top webs so that the WT’s fit up and around the beam flg. and to meet the col. flange, at the top of the beam. I think the OP said there wasn’t much col. moment, so you might not need CJP welds on the col. flgs. to the WT flgs. Obviously, these welds must be designed for the actual conditions. The prep. on the col. section and the WT’s would be done in the shop and the WT’s would be shop welded to the beam. There is considerable fab. savings if the WT’s can be cut short of needing fit-up at the beam bot. flg. too. Fitting a stiffener to the web and the inside of both flgs. is a difficult process, to be avoided if possible. The entire col. load is transferred to the beam web through web to web shear welds and direct bearing btwn. the webs. In this case that direct bearing area may only be (2 x k1)^2. The beam flgs. really can’t take much of the col. load, they are just too flexible as cantilevers in bending, when compared to the web to web shear welds.