(short answer i believe LTC is good)
i am not using these two exchanges so i don't know the fees. but in order to do something like that you need to do these things:
1- check the trading fees of these places
because you will need to pay trading fees 2 times if you want to transfer bitcoin from one place to another using an altcoin.
2- check the price difference and spread in the altcoin that you chose.
if the altcoin has a higher price and a smaller spread you will lose smaller.
for example Doge withdrawal is 1 Doge (~20 sat) but you on one exchange you may have to buy at 22 satoshi and sell on the other place at 20 and that is 10% loss before trading fees! but if you buy something more expensive like LTC at 0.017 and other place is 0.01699 you won't lose much.
3. check the withdrawal fees.
sometimes some exchanges have higher withdrawal for some altcoins!
4. check to see if that altcoin's network is working properly, exchange wallet is operational not in maintenance and make sure you can withdraw.
sometimes these issues do happen.
The easiest way to transfer the amount from one exchange to another would be to convert the BTC to an altcoin which has low withdrawal charge and then transfer it to the particular exchange and then convert it back to BTC or whatever coin you want. Although DOGE is a suitable coin for this task but the price of Doge is too low and even if you sell at a loss of 1 satoshis per coin the change will be a little noticeable. So either of Doge you can use DGB which has low fee and transfers quickly and there won't be any noticeable difference in the amount. You will almost get the same amount of BTC you wanted to transfer to the another exchange.