Generally, you would need a free hand for your focus anyway.
The effect of an arcane focus is that you may use it in place of most material components, but to supply them for a spell requires a free hand to manipulate them anyway.
You would just be going from needing a hand for the components to needing a hand for the focus, be it wand, pendant, or even ring.
Regarding your one-handed warlock, having the hand gone yet being able to cast with the other hand full would be almost equivalent, mechanically, to having the hand permanently occupied with the focus and nothing else (not even the shield from your other question). So balance concerns over casting handless should be minimal, but it’s ultimately up to your DM.