For the My Friend Cayla toy, you can use it without an Internet connection. The FAQ states:
Do I need an internet connection to play with Cayla?
An internet connection will be required to download the free app which unlocks all of the fun things which Cayla can do. Some functions, such as searching for information on the internet (famous people, places, time, weather, etc), require an internet connection. Cayla can do lots offline, like having conversations, playing games, reading stories, and exploring her photo album. In fact, most of the interactive play requires no internet connection at all.
To avoid Cayla sending data to the Internet, simply disconnect the phone/tablet that the toy is paired with from Wi-Fi and mobile data.
The case is similar for the i-Que. From their FAQ:
Do I need an internet connection to play with him?
Yes and No. Some functions, such as searching for information on the internet (famous people, places, time, weather, etc.), and voice recognition require an internet connection. But much of the interaction between the child and the robot can be done OFFLINE including having simple conversations back and forth, playing games, doing brain teasers, and program him to talk or move. In fact, most of the interactive play with the robot requires no internet connection at all.
Once again, to stop the i-Que from connecting to the Internet, ensure that any mobile device you pair with it does not have a connection to the Internet.
The toys cannot connect to the Internet by themselves, so you do not need to worry that they will send data secretly even if your phone is disconnected from the Internet.