Important thing I overlooked: your solution modifies $sBegin!

You would need to create a copy before modifying. One way:

($sEnd) = map {s/hello/goodbye/g; $_;} map {$_} ($sBegin);
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Another:

($sEnd) = map {s/hello/goodbye/g; $_;} @{[$sBegin]};
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A functionally similar solution that doesn't use map:

$sEnd = do {local $_ = $sBegin; s/hello/goodbye/g; $_;};
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Of course, creating a copy and working on it is the canonical solution:

(my $sEnd = $sBegin) =~ s/hello/goodbye/g;
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This couldn't be used in a combination declaration-assignment, though, while the others could.