Slightly OT in that this doesn't address the use of regexen inside a SELECT, regarding which you already have answers. You want to make sure a string starts with $path but the string must not be equal to $path, i.e. it must be longer. You can do that by changing the regex to force it to match a character after $path

$ perl -le '
> $path = q{/ab/cd/e};
> $string = q{/ab/cd/e};
> print $string, $string =~ m{^$path.} ? q{ - Match} : q{ - No};
> $string .= q{f};
> print $string, $string =~ m{^$path.} ? q{ - Match} : q{ - No};'
/ab/cd/e - No
/ab/cd/ef - Match
$
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I hope this is of use.

Cheers,

JohnGG