That may depend on both your phone and WiFi. I have a new Android phone and Verizon FIOS WiFi. When I’m in the house, I’m on WiFi. I can walk out the door and down the block and back, and the transition between cell and WiFi is not noticeable.
There must be a setting to allow you to enter just a phone number without putting it in your contacts.
I do have a problem with the landline phone since it doesn’t have BT. What is the “Acoustic Phone” you had installed?
I believe it was Zebras who first told me about it. On Phonak aids (Marvel & Paradise for sure) you can have your audi set up “Acoustic Phone” as a program (just like I have “Speech in LOUD Noise” and “Comfort in Echo”) which forces the aids to stay IN that program till you hit the button to return to Default or select one of 3 max programs allowed on the aids.
With Acoustic Phone, you can hold ANY phone (cell, landline) up to ONE of your ears and the sound/conversation is actually transmitted to BOTH ears, so it’s almost as good as wearing headphones or streaming a call. I find it absolutely invaluable for the MANY times Bluetooth is acting flaky or if someone just tosses me a phone to talk to someone.
Check it out if you’ve got Phonak aids! 
Yes, and it has to be the same one ear - it is part of the program. Mine is my right ear. It works OK, I’d much rather be streaming. But sometimes (like @1Bluejay says) someone hands you a phone, and says, “Here, talk to Grandma!” or whoever, and you’re stuck.
WH
Yes, they’re Phonak: KS10’s. I just spoke to my audiologist about it. That’s me. I DIY, 
I found it.
Thanks