There's a place on Duke St Birkenhead called Marley's. I'm not sure whether they sell the cigars you're looking for, but I know they sell the American Spirit cigarettes that I smoke, which can't be bought in supermarkets. They also have a branch in Seaview Rd Wallasey.
Turmeaus in Fenwick St, Liverpool although I've never been there so I'm not sure what they stock.
There's also one in Hoylake called Harwoods. Again I've not been there so don't know if they're still in business, however when I rang them I did get a voice message so I assumed they were simply closed when I called.