Hi Stan,
Yes Shiny is incredibly useful when it comes to quick prototyping and getting your R code into a presentable, usable and interactive format.
I usually just set up JIRA sprints with my clients to incorporate their feedback and iterate quickly that way. You can also sync it up to Github via RStudio's built-in integration.
In some cases I've just hosted a Shiny Server myself on AWS and give my clients access that way to specific Shiny apps.
Happy to help or answer any additional questions if you'd like,
Tanya