I've seen some very good lefty shortstops. It's not the ideal, but if the player is athletic enough she can be very effective. For 10U rec it should be fine. Eventually she will probably need to change positions, though, unless she is just amazingly gifted. For now, though, if she's your best option there I'd say go for it.
Not sure if it will matter that much in 10U REC ball, but if I had to choose between playing a lefty at 3B or SS I would chose 3B simply because SS has to be able to take throws from the catcher on steals. Lefties can pitch, play 1B, play OF, and catch before they play MIF or 3B. Also, if I had 4 lefties on my 10U REC team the first practice I would line them up and see if you can teach them to pitch!
At 10 rec - if they can make the throw then I wouldn't think twice about putting them there.
Though in most 10U rec leagues, 2B and 1B are the most important players in the field after pitcher/catcher. You need someone who is going to catch at 1B and someone who is going to make all the easy plays at 2B where a lot of balls get hit for what need to be easy outs. If you have players who can make the throws from SS/3B after that, that is a bonus. We won a lot of rec games with a good right side of the infield, a RF playing shallow to gets some extra outs at 1B and a pitcher who didn't throw all that hard but could throw a lot of strikes on the outside half of the plate.
Too many 10U rec coaches try to hide a weak fielder at 2B when they should be hiding them at SS/3B especially in leagues where you have to give everyone some infield innings. In rec, if they hit the ball to 3B I can live with the hit and outs are almost a bonus, but I need the ball hit to 2B to be an out at 1B every time.
JAD - 2 lefty pitchers! 1 starter, and my daughter as backup.
Riseball - my daughter also catches. lol
Basically, my starting pitcher and my daughter can play anywhere you put them. It may not be their best position, but the know how to play it. My problem is my little short stop. She is quick, but throws all over the place. I was considering moving my daughter from 1st to SS or 3rd, if I can get lefty #3 to hustle at 1st. Lefty #4 plays RF.