8 – Is it possible to do Drupal Development without a local development environment?

I am used to having Virtualbox and linux running on my local to do development work. My new client has a migration project for me to do but they do not allow any local development tools like xamp, dev desktop, Vagrant, Virtualbox. They are a government client and they want us to use their laptops and work on their network in their office. They are not very tech savvy They also do not want to use Git. The client asked that I do all the work on their staging redhat server then clone it to the production server. Their project is to turn 2 static html websites into Drupal CMS. The sites consist of a 80 pages and about 200  PDF files that users search for and download. Does anyone have any ideas of how to approach this project? We cannot place their website content on our personal laptops. But I should be able to build the theme and content types on my personal laptop. 

My plan was to let them install Drupal 8 on the stage server. Then I will download the site and sql file. Copy the site over to my personal laptop which has Virtualbox. ( I will need to get permission to do this) Then build the subtheme, content types and add the needed fields to all content types. Basically get it ready to import CSV spreadsheet. Export and import these changes to the stage server and upload the new theme. Then create the CSV spreadsheets based on the clients website pages and pdf files. Create the migration scripts and import content directly on the staging server. That is what I though I could do. If you have ideas please let me know. Thank you