Do you know if the handset connect ("RJ9") can be plugged into an RJ11 connector. I'm not sure of the dimensions and no longer have any of them in the house to try out (the landline telephone network is being phased out here).
[Note: I prefer the xPxC description, because there's a lot of "confusion" (fake news/perception) about RJs]
Yes, through very good engineering, the 4P4C plug will fit in, and connect properly to, a 6P socket (and to an 8P socket).
I would advise against that for outdoor applications, because the vacant space at each side of the connector would be an exposure. (Keystone jacks are available in 4P4C, if you really want to go the "jack" route)
I don't even like it a lot for indoor applications, because the connector is sometimes a little "wiggly"from side to side, which bothers me (but probably doesn't actually matter from a connection standpoint).