Custom wiring harnesses made and sold by yours truly:
http://www.dotheton.com/forum/index.php?topic=47580.0
As for the battery eliminator topic, the short answer is, "No. You can't do it with a CB350".
Longer answer is, "Probably not, but you can make some changes that will increase your chances of pulling it off".
The problem with the Honda 350 and 360 twins is that they don't produce enough wattage to run all that's needed. They came that way from the factory. Break even point comes in at 3000 or 4000 RPM depending on the strength of your charging system.
If you really want to ditch the battery and go with a battery eliminator (which is basically a large capacitor), you need to reduce the amount of power your bike uses and/or increase the power output of the charging system.
The first is much easier, but the second is also worth considering.
To reduce the wattage requirements, your best bet is to pull as many lights as possible. LED replacements are also an option assuming you need/want to keep some of the lights. Access to electronic ignitions that can decrease your dwell also work, as does higher resistance coils. Though I advocate the change to a new regulator/rectifier as well, I have no evidence that it will decrease your wattage consumption. All wires should be examined and cleaned of corrosion and dirt.
To increase your power production, you have a few choices. Most common is to pick up an aftermarket stator such as the one available from Rick's Motorsport. Many alternator specialist shops can also rewind your existing stator (more coils in the stator means more power) as an upgrade. If you wanna get a little crazier, you can try something like this: http://www.dotheton.com/forum/index.php?topic=38872.msg500741#msg500741
After each change, you should test to see if you've hit your goal. This is simply done by hooking up a multimeter to your battery with the bike turned off and with the battery sitting (without being charged or having the bike run) for 24 hours. Your reading should be somewhere around 12.5V. Now start the bike with the kick starter are let the bike idle until warm; about five minutes or so. Measure again. If you're at 13V or better, pull the battery and stick an eliminator in there; you're good to go.