Hesitation noise and how to write it? In English when thinking (and sometimes when unsure) we use the filler word "uhh" (sometime written as the variant "er"), pronounced as a prolonged /əː/.  What sound is used in Mandarin, and how is it written?
Interesting question. 
There are some dictionaries （e.g. this and this) that list this character:


  呣 m2 or m4


as being an onomatopoeic word used to express a humming sound one makes when thinking. And yes, that would be an "m" sound with 2nd or 4th tone. I recall having seen other sources listing also 呒 m2, even though this is also used some times as a contraction of 没有。

I believe the key point is that western languages regard onomatopoeias as "naive" words that kids use, because they resemble sounds and are easy to learn. Whereas sounds in Chinese are often represented with dedicated uncommon characters or even words, e.g. 潇潇 （xiao1xiao1, pattering of light rain), and therefore confined to the written language. Personally, I've never seen any of those in colloquial writings. 
When people text me over Wechat that they have to think, they just write 我想一想 or something on the line.