Be nice seeing this come together.. Got a bit of a soft spot for the Beattie WT's after I fired one of them at the Epping Ongar last year.
With regard to soldering irons, I'd be tempted to purchase a 25w and see how you get on with it. It's very definitely horses for courses with soldering irons and temperatures, preferred flux etc, but get yourself a 25w and see how you get on with it. If it's not man enough for the job, but something with a little more oomph. It's a small investment in the grand scheme of things, and it will always be handy in the future for small details and general electrical wiring too.
If you need something with a little more heat (which personally on thin flat WM I'd be surprised if you do) I'd highly recommend a Weller 40w iron. Just make sure you chuck away the tip that comes with it and invest in a high quality tip. The better tips are around £10, so an extra investment, but the standard tips burn away in no time, whereas I've had a decent tip last me around 6 months of solid soldering if you look after it.
JB.