You don't seem to realise that TB and the BTYahoo option are 2 completely independent things. You can utilise either, both or none as you wish.
The BTYahoo option is just another email a/c, that BT are offering you, that may be accessed many ways, including via TB or Webmail. You don't have to use it.
All you need do is change the Outgoing SMTP Server to port 587 Authenticated in TB on your existing account, to stay as you were.
There seems absolutely no advantage in taking up the BTYahoo a/c when you already have a Yahoo a/c, esp. as you would need to inform everyone of your new email address.
1999: Freeserve 48K Dial-Up => 2005: Wanadoo 1 Meg BB => 2007: Orange 2 Meg BB => 2008: Orange 8 Meg LLU BB => 2010: Orange 19 Meg Tweaked / 16 Meg Untweaked LLU BB