D.T.
Babies don't need teeth to eat anything! Babies don't use their teeth to eat - the front teeth is used to take bites off. Molars are used for chewing and those rarely come in before the first birthday. None of my kids had a single tooth before their first birthday (which is still well within the range of 'normal' but most people don't know that). However, by 7-8 months, all my kids were 100% feeding themselves with their fingers (they HATED to be spoon-fed) because they were independent and insisted on doing it themselves. By 7-8 months, they were just eating whatever the rest of the family was eating at a meal but it was cut into pea-sized bits (since they lacked teeth to take bites off).
Since your son is 10 months, just cut-up whatever the rest of the family is eating and put it on his plate/tray. Pretty much everything can be a finger food -- even lumpy oatmeal. It's messy, but they develop GREAT fine-motor skills early on and the messiest part only lasts for a short while until they get better. If fruit/veggies are slippery, just crush up some crackers or cereal like cheerios into 'bread crumbs' and roll them around in it.