Are there any whiskys that one can recommend that are smokey, yet not overpowering with the raw alcohol kick that Laphroaig gives?
Welcome to the forum. The Lappy QC is a little rough around the edges imo. The 10yo would be more approachable for an inexperienced palate.
Many people jump in at the deep end and just go for the big peaty ones, in fact they are the gateway into whisky for many. Lagavulin 16 goes down easy and is the easiest Laga to find (they do a more expensive 12yo that has more punch), there are many Caol Ila with varying levels of peat/smoke and Caol Ila is another great distillery. Ardbeg is fantastic stuff imo, the 10yo and Uigeadail are as good as peatsmoke gets for the money.
So they^ are the big four i suppose (all from Islay), Kilchoman is also heavily peated and located on Islay, and Bowmore and Talisker are down the peat scale but offer smoke.
Longrow is heavily peated but less pronounced with smoke, more farmyardy (and very nice). Other distilleries are offering peated batches like Benriach or Bladnoch but you will need to double check your buying a peated bottling.
Hope this helps.