We always have threads on sleep problems, its mostly recycled info, but helps out newbies. This however is something I never seen here.
I have slept with a small floor fan just for the white noise for 20 years. Worn a lot of fans out LOL 365 nights a year. Even took smaller fans on travel, and compact battery for camping (but thats for air and white noise).
People who also slept with real fans for years give great reviews on this and say its even better. Plus you can take it camping, battery lasts 16 hrs and is USB rechargeable.
Looks like its under 3x3 inches, different fan noises are all digital recordings, so no fan blowing air around.
/www.amazon.com/LectroFan-Wireless-Sound-Machine-Bluetooth/dp/B01LBVLBKY/ref=pd_sbs_121_2?_encoding=UTF8&refRid=9627DKWZ2EEHE6HAGHDE&th=1LectroFan has a plug in version too, which is linked in that above Amazon page.