Oh, poor Wallee!. It is strange that he does not like to walk. If you have tried different types of harnesses and he still does not like ti then I just don't know. Seems like he would enjoy going out with your other dog.
If it really bothers him then maybe he should just stay home. Maybe staying home and missing out while your gone will make him reconsider!

If not, and he is happy staying home then just let "sleeping dogs lay."