LS, it's not that there's NO chance, but it's very unlikely. There is less chance of choking on finger foods than on spoon fed mush. And you should always supervise them when eating jic, but it not likely to be a problem. Certainly neither of my boys have ever choked.

If you haven't done a first aid course for parents/carers, it is a good thing to do for a variety of reasons, including learning what to do if they choke. St Johns and Red Cross run them, and mostly likely other organisations too. Might give you some peace of mind?