may help you . You need both settings - isolated shared library and PARENT_LAST classloader setting to use your own httpclient libraries. PARENT_LAST is required to override classes provided by the server.
Any of those help Try using "parent last" classloading so that you use your own classes instead of the ones from WAS. Change it for the application and depending on your configuration for the application on the webmodule as well.
wish of those help Httpclient libraries conflict with WebSphere provided. Please try to create isolated shared library via Environment > Shared libraries, put the http client jars there and map that library to the application. See more details in this post WebSphere 8.5 and Apache HTTP Client
it helps some times A NoSuchMethodError indicates that classes available at runtime are different to those used to compile your code. It usually boils down to having multiple versions of the same class on the classpath. Double check this for the class in question and remove the unwanted version.
To fix this issue I think a fixpack upgrade will fix this for you. WebSphere has an internal copy of the Apache HTTP client (used by its JAX-RS implementation) that was visible to installed applications until fixpack 184.108.40.206. If you want to use your own copy on a fixpack prior to that, you'll need to utilize PARENT_LAST class loader delegation or an isolated shared library in order to make sure that the class loader loads your own copy of Apache HTTP instead of WebSphere's.