Could a Hexblade warlock be plausible in a low magic campaign?

I am planning on running a low magic campaign for my friend group, wanting to try a more gritty style campaign, and have an excuse to use the renaissance guns from the DMG. I ruled that I would allow magic as long as it was logical for the setting. For example, since the artificer class cast their spells via little gadgets and stuff, I ruled that as ok. One of my players reached out to me about potentially playing as a Hexblade Warlock, and they seemed pretty excited about it. I’m having trouble seeing as to how I could integrate this high magic character into the setting I made. I know that a hexblade is more combat-oriented, but I haven’t really been able to explain the eldritch invocations or spells outside of Eldritch Blast. I don’t want to just ok it without explanation, but I also don’t want to just shoot then down. I was considering seeing if they would mind playing a fighter with a sentient weapon, but I figured I might ask here first to see if anyone has had a similar situation or has any potential solutions.