An internet search for “remote control outlet” should return results for a fair number of finished-goods consumer products that allow control of an AC circuit using a remote control device, and small AC fans are likely also available at many of the retailers that would carry such products. Such an approach would likely give you a reasonable result for less cost and effort than assembling a solution from component-level products of the sort which are Digi-Key’s primary product of trade. Standard ceiling fans with remote control features are also available, and might be a good option if space permits.
Small-diameter fans don’t move a great deal of air, and tend to make a relatively large amount of noise in the process of doing so. They also consume a fair bit of electricity, so a battery-powered unit likely to give a decent result in terms of comfort level would probably require frequent battery changes, and prove unsatisfying from that perspective.
This said, if you would still like to pursue a more build-it-yourself sort of solution, FOBLOQF-4S1-ND is a single-channel remote control device which might be suitable. Similar devices offering multiple control channels are also available.