How to prove strong ties back to country when one is self employed?

Just going through your circumstances:

I am a sole proprietor (a software programmer). I do not have any 'business registration' documents since it's not a company. I work for a company in the USA.

Being a software developer is beneficial in terms that it is harder for you to work under the table. But there will be a greater suspicion that you're coming to find a job - i.e. your real travel purpose is not tourism. Also depending on the nature of your development, you might be able to work from anywhere, which is also a different concern (if you overstay, you'd have enough income).

One possible workaround is to start with the US visa, assuming you intend to also make a visit to the company you work for. Ask them for the invitation letter, and apply for the business visa. This paperwork would help to convince other countries that you do not intend to find work there, and that your employment is legitimate.

I do not own any property and I live with parents so I don't have a rent or lease agreement of a property.

Considering the amount of money you're making - which is very large for India - you might want to address this. There's a big difference between living with parents because you need to take care of them, because you choose to, and because you cannot afford to rent a place. If you need to take care for your parents, this may be a tie, but you will also need to prepare to explain who'd care for them in your absence.

Do you own anything else? A car, for example?

My wife is already in the UK completing her Masters and will return back after that is done but, obviously, there is no way to prove that.

This, of course, is not helpful, especially for your UK visa. Expect questions why don't you want to stay longer with your wife ("you're a software developer, can't you work from UK?")

I do not want to apply for a dependent Visa as I have NO intention to stay there as my contract will not continue with the USA company if I shift now.

A letter from your employer company stating that would be useful.

I have sufficient income proofs as bank statements and income tax filings ($4000 per month).

This is good, but not a tie obviously.

I have no dependants in India, parents (self sufficient) or children to look after.

In short, you have no obvious ties to India except your parents. But there may be non-obvious ties. Ask yourself, if you visit US and the company you work for tells you "stay in US, we'll get you H1B", is there anything which would make you refuse this offer and return to India? Planned medical procedures, family trips, friend weddings to attend? Any future plans involving India? Any future travel plans, including prebooked travel, originating from India, which would happen after your return from US? Those may be your ties, and while not as strong as if you left sick parents, and a wife with five kids there, it may be helpful.