Breaking the touch barrier advice

So me 27M and my date 29F have seen eachother twice now and we have a third date set for tomorrow but the problem is even though the dates have been good we still havent really broken into that touchy/flirty side of things just yet

Our 3rd date will be at an arcade and she says she really likes crane games, what are some ways I could potentially engage her with using forms of touch and flirting?

What I was thinking of doing is immediately when we meet at the entrance I could maybe stick my arm out so we could lock arms and be side by side as we walk around the place so i could maybe set the vibe right off the bat, would this be too bold of a move?