Please also refer to our blog post here: https://medium.com/@Ledger/what-would-happen-for-ledger-hardware-wallet-users-in-case-of-a-bitcoin-fork-3b955a065d57
Our official position on forks is that we advise our customers not to issue transactions before the dust settles (i.e. there's a clear majority). Following that we'll offer solutions to track non majority chains if that makes economical sense and if there is enough demand for it (for example right now we're offering a wallet for Ethereum Classic).
That being said, power users might want to trade between competing chains in the meantime. We'll provide unofficial advice for our users to do so, at their own risks. It's not quite sure how this will plays out if it happens (which tools will be deployed, if there will be anti replay mechanisms and so on), but it'll likely be one or a combination of the following: