The best option will be to migrate your application to support JSF 2.2, which shouldn't be terribly difficult. There is some IBM documentation here for migrating your application from JSF 1.2 to JSF 2.0. Since your application already uses Facelets, however, you should be able to migrate your app via configuration changes; the instructions in this answer will probably be more helpful.
It is also possible to configure WebSphere to use a third party JSF provider - in that case, you could provide your own version of JSF 1.2 for your application. Documentation for that is here
Instructions for providing a custom JSF implementation:
Add the third-party listener to the web.xml file.
Add the third-party JSF implementation Java™ archive (JAR) files and its required dependant JAR files to the application as an isolated shared library and associate it with your application:
Move the JSF JAR files and all third-party libraries referenced by the JSF JAR files and UI component plug-ins (for example, PrimeFaces) to a directory outside of the application.
Create the isolated shared library. See topic Creating shared libraries for information about how to create the shared library.
Ensure that the classloader is set to PARENT_FIRST, the default value. To view the current configuration in the administrative console panel, click Applications > Application Types > WebSphere enterprise applications > application_name > Class loading and update detection.