The point of finger foods is to help them learn to eat real food. I think what might help is to think of what size and shape real food (that you would eat yourself is) and give it to them in that size. Most food isn't the size of a rice crispie and most adults would struggle to eat it with their hands if it was. (Personally, I think your doctors advice sounds kinda crazy!). Just offer them finger foods like you would eat. A piece of toast with whatever you'd eat on toast, pasta with sauce, apple slices, a banana (I always cut into 3 pieces so it wasn't huge and more easy to manage), a small chicken leg, pieces of baked potato, steamed vegetables in whatever form you'd usually have them, soup with bread to dip in it, etc. Usually it's easier to start with finger foods that don't require a pincer grip, but would be held in a fist, so think things that are stick shaped. Or also, things they can dip their hands into and scoop into their mouth or lick their fingers (yogurt or porridge are easy, but also soups). These sorts of things help them to learn to control finger foods in their hands as well as their mouths before they are shoving things in that might actually slip down before they're ready to swallow them - because things like 1/3 of a banana or a cucumber stick or a roasted carrot stick sorta have a handle they can hold onto while they chew. You'll be amazed what they can chew with their gums. They don't need teeth. My daughter didn't have any teeth at all when we started and she was eating toast and baked potatoes and whole bananas and roasted veg at 6 months. My friends daughter ate 4 strips of roast chicken on her own the first day that started weaning. They really can do it. But the hardest bit at first is just being able to pick things up. So I'd stick with stick-shaped foods or yogurt/porridge/soup for dipping fingers in at first. But if they do seem to have a good pincer grip or can at least have go, you might also offer things like peas or blueberries or halved grapes. My daughter was eating these from about 9 months, but she'd had 3 months of practice with finger foods before that, so it might still take a bit of time for them to be confident with their pincer grip. Basically, pureed or mashed foods that aren't in their normal form are for spoonfeeding (if you want to spoonfeed), but I would think of finger foods as just normal foods, in their normal shape and size like you would probably eat them. If you think of it like that, you might find it's easier for them to pick them up and get used to eating them rather than trying to dice everything up too small, if that makes sense?
To give you an idea, my daughter's first ever meal at 6 months was mashed potato, roasted carrot and parsnip sticks, and a yorkshire pudding. She also used to really like toast with mashed banana or avocado (or sometimes both together), cucumber and melon sticks, and muffins (think like banana bread muffins or carrot and apple muffins, just made without sugar). She was eating all of that without teeth too, but the main thing was that they were things that were big enough she could pick them up easily.
