My company is preparing a new production box while the current one is running. I would like to proactively install applications in Tomcat container of the new production box
You can simply rename de WEB-INF directory inside the webapp that you don't want to auto-start to some other name like Disabled-WEB-INF, before starting tomcat.
Later on, if you wish to start that app, while tomcat is running, simply rename back the directory to WEB-INF.