Facts to support theory that Shanks must have a DF power:
1) The only other Yankou shown thus far, Whitebeard, has complete mastery of all three forms of Haki and has a very powerful devil fruit.
Shanks is one of the other Yonkou, one of only 3 pirate captains who can legitamtely call himself his rival, thus on top of his long evident mastery of Haki, he must also have a DF power to match Whitebeard’s.
Seeing as how the Yankou are in a stalemate type situation in the grandline with each ruling their own territory, and each being roughly equal in fighting power (Kaidou’s attempted attack on Whitebeard and Shanks successful interception of Kaidou is evidence of their proximity of strength), makes it a good guess in my opinion.
2) Shanks loss of an arm did not prevent him from becoming a Yonkou, but it led to Mihawk not wanting to duel him anymore?
Obviously Shanks did not have a DF ability when he met Luffy as he swam to rescue him. Mihawk once duelled with a young Shanks, but ceased to do so because he was not interested in fighting a one armed man (presumeably because he thougth it wouldn’t be fair), and yet Shanks managed to become a Yonkou anyway despite one of his rivals in swordsmanship not seeing him as challenge worthy anymore (at least in regards to swordfighting alone). Thus if Shanks handicap did not prevent his from becoming on par with Whitebeard he had to have gotten a serious boost in power sometime between loosing his arm and now.
**3)**Shanks’ encounters with Blackbeard at different points in time.
We now know that Blackbeard gave Shanks his trademark scar at some point in the past. Shanks has a healthy respect for Blackbeard’s strength as a result of Blackbeard facing Shanks in direct combat. At Marineford Shanks issued a challenge to Blackbeard and Blackbeard said it was not time to fight Shanks yet, despite having had the strongest logia ability for some time, and just acquiring the strongest paramecia. This leads me to believe that Teach and Shanks fought on equal footing before either of them got a DF ability, and Blackbeard’s hesitance to fight Shanks despite two DFs is because he felt he needed total control of not one but to DF to be able to deal with Shanks, who presumably has mastery of a DF power that Teach knows about.
4) Prodigous Haki abilities are not enough to merit Yonkou level strenght, nor is mastery of a haxxed DF ability, so Shanks must have a combination of both.
Crocodile and Ace were both easily defeated by Whitebeard, despite having great DF powers. Boa Hancock has access to all three forms of Haki and has a DF ability, but counts the 7 Warlords as her peers. The 3 Admirals also have great DF powers and clear mastery of Haki, but were hesitant to step up and face Shanks when he challenged them.
There you have my two cents. Feel free to poke holes in anything I’ve said or ask me to elaborate. Cheers.
Clarifications/Rebuttal:
It seems that most are citing Garp and Silvers as examples of why you don't need a df ability to be elite. I would like to respectfully point out that these two reached their peak 20+ years ago. The standards of strength have changed. I don't think Haki alone can cut it anymore. When Roger uttered his famous last words the OP world experienced a pirating boom which lead to more pirates on the high seas constantly fighting for glory and riches, a survival of the fittest type scenario. As a consequence I believe with more people out exploring the grand line, and more DFs being found as a direct result, an arms race of strength began. The Yonkou are a product of this arms race, complete with vast amounts of underlings they drafted into their ranks and elite crewman. These underlings may have been drafted by force (like Ace did with Doma and various others), and elite crewman want to be at an extraordinarily strong captains side no? Thus a strong fleet and elite crewman may not necessarily take away from the Yonkous individual strength but might very well be a testament to it