Is it possible to avoid triggering a means-plus-function style rejection for a claim that does not utilize "means" language?

Yes. 

Phrasing the claim in this format:

"A device comprising:
a processor; and
a memory storing instructions that, when executed by the device, provide a system comprising: "

will usually avoid a 112(f) rejection.  Note that there is a small tradeoff with this phraseology -- the system is required to be implemented with the device.