For BLW the size is more preferable to be bigger rather than smaller, the size of an adult finger as a guide. It needs to be big enough so when they hold it (pick it up on their own or if LO finds this too frustrating in the early days you can hold it up and let them grab it) half the finger is in their palm, grabbed, the other half or so is sticking up out of their grasp and this is what they eat. Generally larger pieces are hard to choke on, the idea is that if they can manage to get a bit in their mouth they are fully aware of what went in and can manoeuvre it more successfully. An example, I gave mine a half apple or whole apple never slices, he found slices broke off in chunks and harder to work with where as once his front teeth were in a whole apple was 'grated' by the front teeth.
If baby doesn't manage to chew they will more likely spit the food out and possibly have another go at it or at another piece.
No need for teeth, gums are super hard and can manage just about anything, even strips of meat which they gum and suck at until there's only strands of connective tissue left.
Gagging is quite common but different from choking, the gag reflex is further forward in a baby which protects the airway, don't panic or if you do don't show it. LO will likely gag, bring the food forward and continue eating or spit it out. Couple of times mine swallowed a piece too big (he was a hungry boy!) which brought on a vomit, pretty clever their bodies to do this, and pretty gross but he'd just pick up the vommed lump and eat it again.
During a choke they stop breathing and look panicked immediately, where as a gag they tend to look ok and are still breathing, maybe a bit watery in the eyes.
Look into a paediatric first aid course if you are concerned as they can show you the correct way to respond to a choke. Hitting on the back is not the best idea as it can cause a choke or move the piece into a worse position. The only choke experience I had during BLW was a grain of rice slize slither of kiwi I licked off my finger after popping the rest of the kiwi (in quarters) onto DS's tray. it caught in my airway and I spent several minutes desperately trying to breathing in enough air to cough the thing out.
With avocado I suggest halving to remove the stone then cut (thickly) across the pear to produce a crescent moon shape (well sort of), avocado is very slippy to pick up but the notch shape where the stone used to be is a good place to help grip. You can do this with other foods too, cut crescent shapes to help the grip.
I avoided sultanas, grapes, cherry toms, peas, all small round things, until I felt he had sufficient control, again once the pincer grip is in to pick these up then in theory they should manage. Green beans, asparagus are naturally a good size.
Sorry Tracy, don't want to shoot you down but WRT your last sentence, just want to mention that in the UK traditional puree weaning starts at 6 months and it is advised the time table goes very rapidly from puree to mashed to lumps to regular family meals AND that finger foods are offered along side all of these different weaning stages, from 6 months. So whilst I agree that in general you choose one method or the other finger foods are an integral part of the traditional weaning routine these days. It seems that people often stay on purees too long and that's where there might be some difficulty with moving on, or baby liked the puree but doesn't like lumps so offering finger foods alongside helps them learn the 'real' texture of food and to join in with family meals. Many areas here now the health visitors advise BLW rather than tradition puree weaning.
Certainly the BLW process is about learning about foods, especially foods which are normal for your family, rather than how much you can get them to eat so don't worry at all if not much goes in or if LO prefers to mush it in their hands and draw on their tray with it, it's all learning.
For sloppy foods you can pre-load a spoon and let LO pick it up, or take it from your hand, or let them pick up fist fulls of it. Mine had a monster feeding session with humus one day, couldn't get enough of the stuff, just grabbed it and shoved it in his face
Of course you can make it slightly cleaner by spreading on pitta bread instead, although maybe not quite as hilarious for mummy