How about, instead of deleting Mycelium, you first install it on your new phone? Or, if you don't have a new phone yet, create a new account (or use a "Guest" account) on your current phone and install Mycelium there (I've only tested this on Android). This way, you can see for yourself that you won't lose things before actually deleting data.
It's like any backup: don't just trust it, but test it!