You do not use the Wallet or a Contract if you just want to send someone some cash.
To send ISK to a character who is not online
- Locate them in the People and Places panel
- Right click on their name
- Choose Give Money
- Fill in the amount and a reason
- Send it
This works for alts, too.
To send ISK to a character you can see
- Right click on their name
- Choose Give Money
- Fill in the amount and a reason
- Send it