Your chances of winning "Ten in a Day" wouldn't be affected by using the swap function, only if you spend credits. Still, it's not like anyone is going to be winning "Ten in a Day" anytime soon.
Actually, your swap could
mean the difference between getting "Ten in a Day" and not getting it. If you have two incomplete challenges, at any point, that you can't finish (possibly due to failing to get a good enough score in a Daily game...), swapping one out would give you the opportunity to try a different challenge to complete. You can only buy challenges if you have fewer than two incomplete challenges. It's worth saving, except the next two/three weeks, where it doesn't matter. It will take at least 21 days (6 credits a day) to save up enough credits to go for the mini-badge in any case, though, so it doesn't matter right now anyway.