Probably not very efficient, but the best I can come up with at short notice:

$str =~ s/(\S) (\S)/$1$2/g;

Update:See Roy Johnson's comment above on Trix606's similar snippet. Code fixed for single spaces at start and end of string:

s/(\S|^) (\S|$)/$1$2/g;

In reply to Re: Regular Expressions: Removing 'only' single spaces from a string by Not_a_Number
in thread Regular Expressions: Removing 'only' single spaces from a string by BioBoy

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