Ok, after a bit of work I believe I have a solution.

As part of my CI (Continuous Integration) job I run:

cdk synth

I then save the contents of the cdk.out folder to a repository (I'm using Octopus Deployment).

As part of my CD (Continuous Deployment) job I have the following (Powershell):

$Env:AWS_ACCESS_KEY_ID={your key}
$Env:AWS_SECRET_ACCESS_KEY={your secret}
$Env:AWS_DEFAULT_REGION={your region}

$cdk=[Environment]::GetFolderPath([Environment+SpecialFolder]::ApplicationData) + "\npm\cdk.cmd"
& $cdk --app . deploy {your stack name} --require-approval never

So the "cdk synth" will generate the template and assets required for deployment.

The "cdk --app . depoy {your stack name} --require-approval never" is telling aws-cdk to us the existing templates and assets. This avoids a situation where the CD process may produce a different setup than the CI process. The "." indicates that the templates & assets are in the current folder.

You will need to install node & aws-cdk on the CD server (in my case an Octopus Deploy tentacle);

Node install is easy, just log in and install.

To add aws-cdk perform the following (using an administrator powershell):

npm prefix -g  // Make note of the path
npm config set prefix C:\Windows\System32\config\systemprofile\AppData\Roaming\npm
npm install -g aws-cdk
npm config set prefix {original path}

Note that the npm path maybe different for your usage - will depend on the user account used for the CD process and Windows version.