I just got my hands on 3dconnexion's spacemouse and im trying to set it up to work with the forge viewer, i found some JS samples in the SDK for three.js and it works like a charm. from my understanding is that both forge and three.js are using webgl if i couldn't help but wonder if it would be possible to convert some of the code in the sample here to directly work with the forge viewer.
link to the complete SDK from 3dconnexion https://3dconnexion.com/my/wp-content/uploads/sites/63/2020/08/3DxWare_SDK_v4-0-2_r17624.zip
link to three.js sample online https://3dconnexion.com/technical_support/web_threejs.html
Unfortunately, Forge Viewer doesn't support 3dconnexion mouse. You might try to map 3dconnexion's mouse inputs to normal mouse actions and keyboard inputs as a workaround.