On several occasions I tried the portable version of Thunderbird, but it never would work like expected when compared with the installed e-mail client.
But that isn't your problem. MAPI is your your problem. All mail clients support this standard, it allows for a mail message being generated, with the receiver, subject, body text and optional attachment automatically filled in. That more or less leaves one job for you to do and that is pressing the 'Send' button.
It shouldn't matter which e-mail client you use as this standard is supported on all clients.
However, Microsoft, in all their wisdom, made an extended version of MAPI to make a differentiation between their idea of an professional environment (Outlook and Exchange) and well, whatever...(any mail server with any mail client).
Depending on the MAPI functionality that is called upon by the software that wants to report the error, this can become a messy story. For example: encryption on a message-by-message basis requires the extended version of MAPI. Extended MAPI is only supported in Outlook. There are a lot more mail clients nowadays being able to connect to an Exchange Server, but for crap like this you have no other option than to use Outlook. To my knowledge at least.
Also, depending on the requested MAPI functionality, only certain Outlook/Exchange combinations are allowed.
You say you have Outlook 2002 on your PC, a version that is also known as Outlook XP. This is a very old version. So old in fact that Microsoft has already dropped support for the successor of your Outlook client. With that I mean to say that even if you configure your Outlook 2002 correctly, it could still fail just because it is too old (in Microsoft's opinion, not mine).
My usual advice is to just install the Thunderbird mail client as a regular application and you will see this problem go away automatically. Personally, I'm a great fan of portable applications and happily use these on a daily basis. Portable Thunderbird? Don't bother, it's just not worth it to lose your time troubleshooting over. It is only usable when you have very basic mail needs.