You could use driveworks express and just fill out a form in the task pane. Another option could be to create a design table with linked cells that are populated from a form.
As Timothy has said, DriveWorksXpress would be great for this. Unfortunately Xpress does not control equations in SolidWorks, you would have to recreate these equations in DriveWorksXpress, which depending on the number of equations may take more time. If however you are serious about automating design changes in your company and this is one of many parts that could also be automated, now may be a great to to make that switch.
If you would like to find out more, do take a look at our website - http://www.driveworks.co.uk/
Under the Xpress section you will find Sample Projects, Tutorials, How-to Videos and Webinars that you can sign up for.http://www.driveworks.co.uk/products/driveworksxpress/
There is obviously a process of understanding how DriveWorks operates. However this is typically quick as the rules that you create are based on the same syntax used by Microsoft Excel, so there is a strong probability that you will recognise a lot of the rules available to you. They are also very similar to what you have created in your SolidWorks Equations.
If you do have any questions though, feel free to contact me or your SolidWorks Reseller.
Yet another option would be to create a userform with a macro to capture all the inputs and then push that down to your model.