Years ago, I broke my arm in a fall, and needed to move my laptop from my lap to a stand in front of my chair. I connected a small keyboard to it, which I could tolerate on my lap, and I was able to use the laptop that way. I even learned to use my mouse with my left hand for a while, so I can relate to using a laptop with a separate keyboard.
In fact, I got so accustomed to that arrangement, that by the time my arm healed, I still preferred to leave the laptop on that stand, so I could come and go as needed, without putting the laptop down somewhere. To this day, I still use it that way, but the keyboard and mouse are now Bluetooth versions that allow me to control my laptop, my media machine that feeds the TV, and my smartphone for texting.
Having said all that, I'm having a hard time understanding what you want to do, and I've read your post carefully twice. I think it might boil down to this: your separate keyboard doesn't have arrow keys, and you want to remap the h, j, k and l keys (in a certain mode) to act as arrow keys in their place. Is that right? If so, I can relate to that as well.
Many years ago, WordStar was a popular word processor (I wrote two books with it on my Kaypro CP/M computer) that used the Ctrl key with a set of nearby letters to function as arrow keys. Pressing the Ctrl key with a left pinkie finger (it was where the Caps Lock key is today) it was easy to reach that set of keys that represented Left, Right, Up and Down with the index finger, and I got very used to that arrangement. As you can imagine, many other WordStar users did as well. That "Kaypro key mapping" was even used by popular programming editors at the time.
We were all saddened when PCs became the dominant personal computer, and rearranged the keyboard so that we could no longer use the WordStar method we were so accustomed to. But some kind soul wrote a little free device driver that would remap those PC keys to match the CP/M key placements, and we could once again work as usual.
If I'm right, this is something like what you're looking for now. I'm not sure I have an answer for you, but perhaps if we all understand exactly what you need, someone else will be able to help. It might help if you mention the DE you're using, too. For example, most of them provide a way to define keyboard "shortcuts", to issue commands or launch applications by assigning a keypress to them. For example, my Plasma machines all hibernate if I use the keypress CTRL + H. I'm not sure if that could somehow be used to simulate arrow keys, but it might be a place to start looking.
If I've totally misunderstood what you're asking to do, then please clarify, and I'm sure someone can confirm whether it's possible, and how you could do it. Good luck with that!