Ok, sorry for the double post, but here's an update.
I seem to have got the second router working on my network (I plugged the ethernet cable from LAN port to LAN port, leaving the WAN port of the new router empty[hooray for the proper names of these ports, finally!])! However, I have accepted that there will be some security risks. Although I have disabled broadcast of the SSID, restricted access to only my DS's MAC address, and encrypted the connection with WEP 128-bit using a 64 bit ascii password as a base, I still realise these are only trivial hurdles to jump for a determined hacker. That's why I'm going to simply unplug the second router from the mains whenever I'm not using it. This should be a suitable deterrent (it's unlikely someone will try to hack me in the EXACT 30 min - 1 hour window I'm playing my DS!)
I think that's all. The weird thing is though, before I enabled MAC filtering my laptop (Windows 7) COULD NOT connect, which for my purposes is fine, but might be a problem otherwise. In addition, the Belkin settings page says that the internet is 'Not Connected' (which I suppose is due to the fact that nothing is plugged into the WAN port). Hey ho, these problems don't affect me
Thanks for all your help
-Joe