I have fitted an AW into a bike with 130mm rear width and got a reasonable chainline but the width was a bit close! The X-RD3 has about the same length axle as my AW (I fitted the longest one I could get which was I think 6.25" or 6.5"). Sorry to disappoint you but the version with the 185mm axle is the disc brake version, S-RK3. Fitting the anti-turn washers to the inside of the drop-out solves most of the width problem.
X-RD3 is not a dynamo hub! It's a drum brake hub (70mm drum). The dynamo hubs are supposedly more draggy than a Shimano hub and not as well built so your front wheel may be less of a bargain than it appears. Check which model it is, 2.4W or 3W
https://www.sturmey-archer.com/files/catalog/files/307/SPECIFICATIONS%20-%20IGH%20S30.pdf gives the chainline options (measured from the centreline). This appears to be a chain selector, not a rotary one, so you will also have to check for heel strike on the chain/cable. If this poses a problem (like mine!) the solution is to run the cable along the top tube and down the seat stay. Try to stick with 3/32" sprockets even if you go for 1/8" chain, it just keeps the options a bit more open.
In UK SJS Cycles seem to be the principal source for any missing bits and bobs and spare parts (like sprockets)
What style dropouts does the frame have? You will need slotted dropouts to accommodate chain tension adjustment, or an additional tensioner for vertical dropouts.
Is there enough thread on the axle non drive side to add 5mm spacers (dropout thickness is a factor).
Is a matching shift lever available and all the cable couplings.
Is the hub complete - reaction bar (for brake) and reaction washers (for drive) are needed.
Availability and cost of small parts and sundries required to make it work can make a cheap job very expensive.
And then there is the mystery of chainline, adding same spacers to both sides of the axle doesn't change the hubs chainline (which is measured from the center line of the bike). If the hub accommodates a choice of sprockets (flat or dished) that is how the chainline of the hub is adjusted, assuming they are available of course.
^^^ This also!