No, you would not use the qryAppendApplicableQualsToAllExistingEmps. That will reappend all records for all employees. You will have to create a new append query.
It would look something like this:
INSERT INTO tblEmpJobQual ( EmpJobsID, JobsQualsID )
SELECT tblEmpJobs.EmpJobsID, tblJobQuals.JobQualID
FROM tblJobQuals INNER JOIN tblEmpJobs ON tblJobQuals.GrpJobTitleID=tblEmpJobs.GrpJobTitleID
WHERE tblEmpJobs.EmpID=[enter employee ID] and tblEmpJobs.GrpJobTitleID = [Enter Job title ID];
You can use a combo boxes on a form to populate the employee ID and the job title ID & run the query via a button on that form.
INSERT INTO tblEmpJobQual ( EmpJobsID, JobsQualsID )
SELECT tblEmpJobs.EmpJobsID, tblJobQuals.JobQualID
FROM tblJobQuals INNER JOIN tblEmpJobs ON tblJobQuals.GrpJobTitleID=tblEmpJobs.GrpJobTitleID
WHERE tblEmpJobs.EmpID= forms!yourformname!employeecombobox and tblEmpJobs.GrpJobTitleID = oforms!yourformname!jobtitlecombobox