Insert a discretionary line break in the position where InDesign breaks the word. A Discretionary Line Break adds a preferred position to break a word but does not display the usual hyphen - very useful to indicate preferred breaks in long URLs, for example (after all slashes).
From your example I understand you don't necessarily want to have breaks in 'regular' positions. Even with extremely relaxed Hyphenation settings, the word
fox will never be broken as "f-ox". To achieve this effect, I suggest inserting a discretionary line break between every two word characters. That can easiest be done with GREP: search for
\w(?=\w) and replace with
~k is the code for the break).
This will add a break between
o but not between
.. If you need that as well, use
Possibly this is too much for InDesign to handle when done on your "many pages". If you find your computer becoming unresponsive, try an alternative: insert a regular space between the words and set the Preferred Space Width in the Justification dialog to a value as small as possible. For this to work, you first need to change the 'regular' spaces to something else first, because otherwise these would disappear as well - perhaps an en-space does the trick.