My question is do you think I will have an advantage over the neighbor by offering cash via wholesale deal?

Just call them and ask if they are too busy to handle all the work and offer your services.

I opted to offer to sell it to them.

I had a real estate broker license for about 30 years but I never did that full time.Always remember to do the math analysis on your prospects and try to look at them before you make an offer or at least have a clause in the sales contract that allows you the time (usually about 15 days) to make a detailed inspection of the subject property and possibly back out of the deal without a penalty that will excessively hurt you.There is so much to say to you but I am bound to forget something.  

This is the opposite of what I experienced a decade ago when all I was doing was writing offers for people with no money down.

Otherwise, go right to the selling agent with your inquiry.

Even though in my offer, I retained right to cancel at any time during the inspection contingency. 

They will need POF with your offer

I need info on how to properly approach him with an offer. 

Hello, I was offered a kind of paid internship to manage properties for two buy and hold investors who own 35 properties as partners.