You can walk all the way around the lake no problem.
I haven't seen any traveler's checks in years, as you can use debit and credit cards for pretty much everything. I rarely use any cash at all at Disney and you see less and less cash there as everyone is using some sort of plastic.
A long time ago, someone asked a question about traveler's checks in this thread, but I don't recall a good answer as to whether or not there is a place that will cash them.
I have tried to use my debit card in the States but it hasn't worked for me. I will use credit cards for larger purchase but I don't want to use a credit card for a Dole Whip at MK or a drink in the parks. I will start off our trip with some cash but don't want to carry too much so that is why the travellers cheques.