One approach you can take to save the width size of the column is to use the methods toJSON
toJSON will serialize the workbook based on its configuration while fromJSON will load the contents of the workbook. Use the localStorage to store the data.
You can see the approach using AngularJS in this Kendo Dojo by Progress.
For more information, we have a great section in our documentation which goes over storing data as JSON.
Telerik by Progress