Cows milk at 10 mths is not going to have a bad effect, truly - but it would be better if breastfeeding was continuing alongside it. I'm assuming, grouphug, your baby also has other foods as well?
The big thing about no cows milk as a main drink until a year is overstated, in my view - it is a one-size-fits-all which really doesn't stand up to scrutiny as a recommendation for all babies.
The main concern would be iron. The protein in cows milk is virtually identical to the protein in follow in formula or in 'hungrier baby' formula - so no concern there. The iron in cows milk is not especially well absorbed by the baby, but if a baby is having iron in solid foods, and possibly contintuing to breastfeed, then it's likely all will be well - useful to talk this over with a nutrition-minded HV, though, rather than take my word for it as I have no nutrition or med quals (I am a breastfeeding counsellor with NCT).
I sympathise with the desire to avoid formula. It is a highly processed product, with many additives, and which is a hassle to make up from powder. Cows milk is, of course, processed as well, but it is closer to the original item than formula. For a very young baby, cows milk is certainly not suitable (and when it was given to young babies, it had to be diluted, boiled and sugared) and formula is preferable if the baby is not breastfed. But by 10 months, the evidence is most babies will be fine....though as I say, check it out first!