First...I agree with your mechanic. More than 2 weeks could be 2 years...... Even though you intend to return in 2 weeks....like happens....and your return could be delayed.
Even if you run it out of fuel, there is still fuel left in the carburetors. As you are running them out of fuel, you will note when the top carburetor drops out....pull the choke out and the motor will continue to run much longer.
Generally, if this is done...when you drain...a drop will come out of the top carb....a few more out of the middle carb....and a little more out of the bottom. A paper towel is enough to catch it all.
If the Startron is the stabilizer, etc it will help, but there is no guarantee like a empty carburetor...as Racerone has indicated.
If you do not have an owner's manual, you can download one for free from Honda
http://marine.honda.com/support/manuals/models/BF50
Choose one based on your frame serial number.
Now for the fuel connector. The 98 50 HP had connectors with two round ends. If you have a connector that has two round ends, then it is not available any more. You have have replace the fitting on the engine and the one on the hose. They are available as a set. Part # 04104-ZW9-000.
There are aftermarket replacements for the two round fitting...but I have not found any that work reliably.
If you fitting that has one round and one rectangular ends (the new type), then you can order just the hose fitting.....part #17650-ZW9-013.
Hope that helps.
By the way, the 50 has been around a long time and it is a workhorse and will serve you well if you change that oil and gear lube on a regular basis.
It sounds like, in your hands, it will be well cared for.
Mike