A short length of 20 gauge solid copper wire works great for feeder drops to HO scale track. Just bend into a "J" that lays along the bottom flange on the outside of of the rail and add a little flux, the hot tip of a soldering iron and a little solder.
I would use maybe 22 gauge stranded to feed the movable point rails. Be sure to not let solder fill the strands and render it stiff rather than flexible. You might also leave a slight flexible loop. The points don't move much but any wire feed to them must also move.
One other trick with the power routing Shinoharas (and others) is to insulate the feed to the points and frog at the points by slipping a clear piece of plastic under the slider to the points (if there is one). Use insulated joiners at both frog exit rails of the turnout/switch instead of cutting any rail gaps. Then provide a SPDT switch synchronized to the throwbar to connect the points, and frog, and frog rails to the right polarity. [Look for examples on how to add a micro-switch to a throwbar or a Tortoise motor.] A frog juicer can also do the trick provided a decent connection is made at each point or as a loco enters from the frog end of the switch. Not totally "DCC Friendly" as the open point rail polarity will be opposite that of the adjacent stock rail. (I've never found that to be a problem except when there is a derailment already in progress.) Either way the operator must always set the throwbar correctly before the loco enters the turnout/switch.