You could try making the type explicit:

use DBI qw(SQL_VARCHAR);

$sth->bind_param(1, $mrn, SQL_VARCHAR);
$sth->execute();
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Though it would be odd if it does work, because SQL_VARCHAR is supposed to be the default.
Update: The execute() docs say this:

     If any arguments are given, then "execute" will effectively
     call "bind_param" for each value before executing the
     statement.  Values bound in this way are usually treated as
     "SQL_VARCHAR" types unless the driver can determine the
     correct type (which is rare), or unless "bind_param" (or
     "bind_param_inout") has already been used to specify the
     type.
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So that gives some credibility to explicitly declaring the type...maybe the driver is trying to be smart and interpreting your values as numbers, and while Sybase ASE might be able to handle that, perhaps Sybase IQ cannot.