Looking on the internet deeply has found these results:

If possible is the most popular phrase on the web.

if at all possible 1417,000 results on the web	If possible 165,900,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
... COLLOCATIONS it is possible (for somebody) to do something make it possible (for somebody) to do something if (at all) possible (= if it is possible to do it)�... If at All Possible, Involve a Cow is perhaps the finest collection of, and explanation for, college pranks. It is an older book and doesn't cover the nifty April 2006�... Nov 30, 2014 ... "If at all possible" is something of a set phrase, so (to answer your second question first), it would sound odd if you were to change the word�... a new technique that made it possible to perform this operation. if (at all) possible : We need to avoid delay if at all possible. Synonyms and related words�...	It doesn't look like this phrase is very popular! The search could not find any examples on the internet.

if at all possible

1417,000 results on the web

If possible

165,900,000 results on the web

More popular!

... COLLOCATIONS it is possible (for somebody) to do something make it possible (for somebody) to do something if (at all) possible (= if it is possible to do it)�...
If at All Possible, Involve a Cow is perhaps the finest collection of, and explanation for, college pranks. It is an older book and doesn't cover the nifty April 2006�...
Nov 30, 2014 ... "If at all possible" is something of a set phrase, so (to answer your second question first), it would sound odd if you were to change the word�...
a new technique that made it possible to perform this operation. if (at all) possible : We need to avoid delay if at all possible. Synonyms and related words�...

It doesn't look like this phrase is very popular! The search could not find any examples on the internet.