We have found one software suitable in our database for this conversion.
Older spreadsheets from DOS version of Corel Quattro Pro (.wq1) should be still supported in the modern version of the program, so it shouldn't be hard to simple re-save them to some modern format, like Excel's .xlsm files. These are only useful if you will add macros to the spreadsheets, otherwise you can use the standard .xslx files.
It doesn't seem likely that any other 3rd party programs are capable of this conversion, so your only option is Corel Quattro Pro.
WQ1
Files with wq1 file extension can be found as spreadsheets from older MS-DOS version of Corel Quattro Pro.
XLSM
Files with xlsm extension are used for workbooks of spreadsheets created in Microsoft Excel that also include macros, that enhance the functionality of the spreadsheet but some automation features. Other spreadsheets might open xlsm files as well, however they most likely wont be able to use the Excel specific formatting and macros.