I would worry too much about the conflict with the system menu functionality (I assume you mean the "activity monitor" that is dragged down from the top).
A menu from the top would conflict in two ways that I can think of:
1) If the app's menu is open with a swipe action, it might clash with the iOS menu.
2) The similarity in placement, look and feel might cause confusion about which menu is which and what it affects.
To not need to worry about point 1, either:
a) Create a non-accessible swipe proxy (an area where your app ignores swiping) close to the upper edge so that the iOS menu and your app's menu has no overlapping swipe areas.
b) Open it with a button instead.
To not need to worry about point 2:
a) Make the menu appear "beneath" your main view (where the system's menu opens above). This would make it look and feel like the completely different thing it is, even though it has more or less the same positioning in the screen. Slide the main view down and reveal the menu.
About the arrows: If you feel they serve a purpose making the swiping more obvious, have them there and then fade them out after 1500 ms or so. That would give a hint but not ruin the experience. Or add some coach marks.