Well, you can it and see what happens but don't wait too long before trying the more aggressive approach. Shell infections can be very stubborn - once they have penetrated the surface of the shell they are hard to get at.
The best antiseptic wash is something called Nolvasan (or chlorhexadine). Hibiclense is a hand wash for people that contains the same ingrediant and can be used. Nolvasan doesn't require a prescription. You get it at veterinary supply places. Hibiclense you can find at places like Walgreen's. The advantage of chlorhexadine based washes is that they are very gently to living tissue thus speeding healing. Iodine based washes (like Betadine, for example) are also effective. Iodine is harsher to living tissue so a wound may not heal as fast as with Nolvasan but it should heal eventually.
On the salve, silver sulfadiazine (Silvadene or SSD cream) is something of a miracle drug. It's very effective. You can try the over-the-counter salves but if you don't think they are helping, go ahead and see if you can get some of the other from your vet.
The benefit of letting the turtle stay dry for long periods (dry docking) is that the bacteria and fungus that cause shell rot thrive in moist conditions. Dry conditions will help kill them off. When I had to dry dock Spot, I got a large (50 gallon) rubbermaid tub with a lid from Lowes - cost me $18. I kept him in it with some towels on the bottom to make it soft and kept the lid on so it was dark and he would sleep. I put a little dish of water in there in case he got thirsty but am not sure it was necessary. The rubbermaids come with "air holes" so that wasn't a concern. You could do something like this though the temperature fluctuations are a concern. How cold does it get during the day? Could you keep him in a small enclosed room like the bathroom where temps are more stable?

