Or, you're like me and find that shadow detail isn't all that important. Sometimes it can be, but it depends on the picture.
To me the overall appearance of the photograph is a lot more important, and the shadows, while important, are mostly one piece of the puzzle. I find that I often times print so that I have areas of pitch black and without shadow contrast at all anyway, so that losing a little bit in the shadows is far from a disaster. Instead I welcome how those blacks will sometimes support the visual content of the rest of the picture.
There isn't going to be much in the department of shadow detail between HC-110 and Rodinal. But the rest of the tonality will be different. Xtol, TMax, or Ilfotec DD-X will do a grand job of salvaging shadow detail. But if HC-110 and Rodinal is what you have at hand, just try it! Especially if you dilute the developers strongly you will have longer developing times, which will support your shadow details a little bit. Use Rodinal 1+100, for example, agitate every three minutes, and take advantage of the longer developing time to give you more shadow detail.
There are lots of ways to make photographic prints. There isn't anything that is 'correct' in the sense of tonality and so on, so just have fun with what's available, learn how to eke the maximum out of those materials, and perhaps you'll come out like me, finding that I am not concerned with a bit of lost shadow detail. I do, for example, routinely shoot Fuji Acros at 400 and TMax 400 at 1600, because I like the tonality I get. Attached picture is cropped 35mm TMax 400 @ 1600, developed in Xtol 1+1 for 14 minutes, darkroom printed to 8x8" size. Works for me.