Hi! I never played with only one hand, but I think my experience is not too far from it compared from most players: indeed, I do not use mouse for playing but only the keyboard. I use my right hand to move toon around with arrows (do not play with t toggled on, so if I click on left I turn to the left, and not walk to the left while facing ahead), and use my left hand for everything else.
Your main friends are the tab, q and e keys: with tab you select mobs, with q objects, and with e you interact with them. This means that, if you are a non-caster toon, you use e to perform your basic attacks, after "tabbing" till you select your desired monster. Also knowing tricks like pressing b for looting the whole content of a chest are nice QoL hacks.
Beyond this, I've mapped 4 bars to keyboard shortcuts (I'm assuming American keyboard mapping below - even if it's not the one I'm using - since it's the one that most likely you are using):
Bar 1: the usual, 1 to 0; I use it for offensive spells (the stuff you use the most)
Bar 2: the close-to-usual, alt+1 to alt+0; I use it for healing spells (the stuff you might need to click quickly)
Bar 3: the not-so-usual one, alt+q to alt+t, alt+a to alt+g; I use it for utilities, clickies, action boosts etc (the stuff you use a few times per quest)
Bar 4: the even-less-so-usual-one, win+q to win+t, win+a to win+g; I use it for buffs (stuff that you use only once per quest/rest)
Bonus, random button of a random Bar: I set / to horse, simply because it's next to the arrows and, if I'm jumping on a horse, is because I'm gonna move right after that so it's nice to have it here.
I don't use ctrl+keys because those are already assigned to useful shortcuts like enhancement trees, reaper trees, epic destinies or ddo store.
While playing, I usually keep my thumb over the alt key, so that I can move it to the right for hitting space if I need to jump, have it already in position for Bar 3, or just move it to the left for Bar 4. Rest of the hand is usually with index over e, middle and ring fingers over 2 and 1, little finger over tab. The reason why for bar 3-4 I use the first 5 keys of 2 rows, rather than the full 10 keys of the first row, is because even if my hand is not particularly small, pressing alt+p is not super comfortable. Also, I tend to put the most useful offensive/healing spells between (alt+)1 and (alt+)5, since he remaining 5 keys are, again, not so easy to reach. Another useful shortcut is setting the ` key to self, so that if you need to heal yourself you hit that key and right after the desired spell/pot/scroll on Bar 2.
So, as I was saying, I basically do everything with left hand, except moving around. I occasionally hit t if I need to take control of camera, e.g. while swimming underwater, otherwise I always play without it since I don't use the mouse.
Basically, what you would have to do differently from me is moving with asdw rather than arrows - and those keys are right in between all my other mapping, not being replaced by anything else. Hence, even if a bit complicated since you will have to use the same hand for moving AND acting, which means you can do only 1 thing at a time, it does not look completely impossibile to me. Sure, you won't be most likely able to reliably play r10s, but I see no reason why you should not be able to enjoy r1, particularly if in a group!
Hope this will help you, let me know if you have some more doubts!
Cheers