I have some experience with software patents and my basic suggestion is to just work around the patent.
It's very unlikely that they're able to patent something as basic as a swipe to do something.
The patent is likely built upon a combination of a number of things - i.e., a system which sells widgets, which operates on a phone, or a tablet, which uses a swipe to let the user to do X. If you change anything in the chain, your solution doesn't conflict with the patent. e.g., instead of using the technology in a system which sells widgets, simply dispense a sales token the user needs to redeem for a widget.
Another strategy is to simply ignore the patents (better to be ignorant in this case - i.e., don't even look for the patents - or at least make sure your tech team doesn't know what's in the patent). By the time you're big enough to catch the patent-holder's attention, you'll have the resources to either:
a. License the patent
b. Fight the patent
c. Change your solution to not infringe on the patent
The way the patent system works in the US, the patent isn't "real" until it has been tested in court anyway. Passing the PTO's process is just the first step - many patents get thrown out when they're first tested, from what I've heard.
To answer your final question:
Is it possible to move forward without either patenting or licensing?
Yes, it certainly is, and that is what I would recommend. Your main protection is in more traditional stuff - the insights that you have in reaching your market - putting the features together in an elegant way that matches users' needs/desires - the brand you establish.
I believe that people overestimate the value of technology (and thus patents) in the whole equation - sure, that's a part of it, but it's only one part of the whole that needs to come together to make a successful product.
Patents are usually a factor for larger companies - so if you're looking to be acquired, having patents can help your valuation. In reality, my understanding is they're mostly used as threats - i.e., because I have 200 patents in this area, you're not going to go after me with your 150 patents.
Coming at it from where you are (no tech team, just an idea), I wouldn't even be worrying about this - you have much bigger problems to solve before patents should be anywhere on your priority list.