Or are there some stock CFD brokers that only charge through the bid ask spread of the CFDs? I of course understand that in the case of the latter, spreads would be larger.
If you do daytrading you pay no swap fees. But if you do hold the position overnight there is always a swap fee. I would strictly avoid cfd brokers where there is no commission but you pay only the spread, because here you pay a lot more doing some size. Actually best one in the game is Interactive Brokers for stock cfds regarding trading cost and product coverage on stock CFDs.
There are many different CFD broker models, and some stock CFD brokers actually provide trading without CFD interest by utilizing the bid-ask spread to defray costs.