It appears that both the WKS and XLS formats were supported in previous versions of Microsoft Office (2007 and older) and so if you have access to them you can be successful with wks to xls conversion. Microsoft Excel 2010 and later cannot open or work with older Works spreadsheets (.wks), regardless if they come from Microsoft Works or old Lotus 1-2-3.
It is possible that the spreadshee software from the LibreOffice and OpenOffice.org productivity suites might still support WKS format and can be used to successfully convert spreadsheets from wks to xls. The very same most likely applies to Corel Quattro Pro that supposedly still have support for the old MS Works formats.Open WKS file Open XLS file
Spreadsheet program from OpenOffice.org productivity suite
A spreadsheet software application from Corel
Full-featured spreadsheet tool from LibreOffice suite
A popular spreadsheet application distributed with Microsoft Office suite
An older office and productivity suite for Windows