I simply want to transfer BTC into another wallet like LTC.
You just trade the
BTC/LTC pair. It shouldn't be too hard. If you want to actually exchange between your wallets, then you just deposit BTC, trade to LTC and withdraw LTC.
EDIT: If this is not possible how could I transfer my BTC to IOTA using another service? Shapeshift doesn't have IOTA.
Could I withdraw my BTC into CAD/USD then buy IOTA?
I think you're just about the first person ever to ask something like this. Everyone else just trades between BTC and their preferred altcoin on the many available altcoin exchanges which don't even deal with fiat at all.
IOTA is a bit different since it's not on many exchanges but it still
looks like IOTA has a pair with BTC, and it can be traded on IOTA's own exchange as well.