Converting .wq1 files to .xlsx format.
The newer version of Corel's WordPerfect Office (formerly known as Corel Quattro Pro) still supports older spreadsheet files (such as .wq1) from Quattro Pro's DOS version. It shouldn't, therefore, be too difficult converting/re-saving them to newer formats, such as Microsoft Excel Spreadsheet (.xlsx).
We are, unfortunately, not aware of any software, other than WordPerfect Office, capable of converting .wq1 to .xlsx.
A spreadsheet software application formerly known as Corel Quattro Pro