I had a hard time generating that error.

$ find . -name "doesn't exist" -print

$ find . -name "" -print

$ find . -name -print

$ find . -name
find: missing argument to `-name'
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There's no way the command you're executing could generate that error with my find. Maybe if $k contained a newline and you hadn't used quotes.

Anyway, if you want to avoid unintentional interpolation, use IPC::System::Simple's capturex.

my $output = capturex(find => ( -name => "$k*", -print ));
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By the way, "\*" is the same as "*".