Q:

恥知らず【はじしらず】 versus 厚顔無恥【こうがんむち】

The lack of examples makes me difficult to understand well the difference between 恥知らず and 厚顔無恥. Both seem to mean "shameless".
For example, can I use both as follows? Are there any differences?

脱いだまま公園で散歩する人は恥知らずだ。
  脱いだまま公園で散歩する人は厚顔無恥だ。

A:

「恥知{はじし}らず」 is an originally Japanese word (大和言葉{やまとことば}) as you could tell from its reading/pronunciation.  (Please do not be fooled by the use of kanji (恥 & 知).  The kanji were just "assigned" to the word later on.  Japanese was only a spoken language before we encountered the Chinese and started learning the kanji and created the kana.)
「厚顔無恥{こうがんむち}」 is, of course, a straight-up Sino-loanword.
Just like the million other Yamato-Sino word pairs, there is little to no difference in the basic meaning.  
The difference that does exist is that the Sino counterpart tends to sound more formal, more academic, less intuitive, etc. than the Yamato counterpart. 
Finally, the general differences between Yamato words and Sino loanwords are strikingly similar, IMHO, to those between English-origin words and "big" Latin loanwords used in English - begin vs. commence, worker vs. employee, put out vs. extinguish, go down vs. descend, etc. 

A:

These two are basically same meaning,so either one is fine in this situation.
To be exact, for me, 厚顔無恥 sounds a bit stronger than 恥知らず, but Japanese don't care the differences so much.

