Swipe to delete or "remove from view" is slowly becoming an accepted gesture in the mobile community. As mentioned in other responses, this action is already common on iOS, many Android phones use swiping to allow users to dismiss notifications, and even the Gmail uses swipe to archive emails and remove them from the inbox. So although it may not seem intuitive as a stand alone action, it is building off of other 'interactive languages' that users have already become familiar with by interacting with several other applications. As long as the visual language communicates that an object can be deleted, it is likely that users will immediately resort to gestures that they are already familiar with and you will probably not need a prompt.
A general concept in UX is to build off of what people already know so they don't have to learn a new 'interactive language' for every program they use, and so you don't have to reinvent the wheel; especially if it's a common action that most apps have such as save, close, and delete. By this point in time in mobile development, plenty of research has been done for common interactions and gestures which big companies, like Apple and Microsoft, use to create interactive interfaces. If the majority of programs are not using shake to delete, someone has probably proven in research that it's not the best UX practice, so it's more than likely not a good idea to use it in your own app.
One last tip: Although using common best practices is a good way to get started in the right direction, it is always a better idea to test out application interaction. Testing can mean grabbing a few people who know nothing about the program and just asking them to carry out simple tasks while doing your best to remain unbiased and not lead their actions (without using action terms like click, tap, swipe). If you hand this program to someone and tell them to delete an item, see how they try to carry out that action: if they're all trying to swipe, then use swipe; if they try to tap and hold. use tap and hold. On the other hand, keep an eye out for disruptions in their experience: if they accidentally shake the phone and it deletes something, don't use shake; if they don't read the prompt and just start swiping, then you probably don't need it; or if they can't figure out how to delete anything at all, then explore other options.
Sorry for the long winded response, hope this helps!