First step will be to configure the different environments in Workspace so you will be able to toggle between Development connection strings and Production in the designer. This can be done from Workspace > Management Console > Environment Library > Templates >Environment Fields.

Once this is done, you can toggle between the environments in the designer, choosing the target environments variables to be used in the deployment. If the Client tools machine is able to connect to Production, then you can toggle to production and deploy from the designer. Alternatively create a deployment package and deploy using MSBuild. NOTE: if deployment packages are used remember to build the process using the target environments settings.

Some references:

http://help.k2.com/en/k2blackpearluserguide1420.aspx?page=Create_Deployment_Package.html

http://help.k2.com/en/K2blackpointUserGuide4.6.aspx?page=Examples_MSBuild_Usage.html

http://help.k2.com/en/K2blackpointUserGuide4.6.aspx?page=MSBUild.html

HTH

Vernon