Client wants me to sign a contract after 1 year of working together, cites US tax laws as the reason

Question

I'm a software developer freelancer, I have a client I have been working with for a while now (a year on the last projects, but many years before as employer-employee) which recently cited tax-law related issues due to which we need to sign a contract on the work done so far (in the last year).

I "am" a Croatian 1-man company and the client is from US, an Inc. with a couple orders of magnitude more money then I have but not really a fully developed corporation with it's legal department etc. I generally work only with people I trust, and on handshake & trust basis, contracts excluded, judging that:

1. if it comes to litigation, the client is lost, this is the biggest damage that no litigation will reverse
2. if the client rips me off, I will not be able to recover my lost money through litigation because the fees are generally too low for a good lawyer to handle and for me to still have any money left out of it (~40.000$ per year, court on a different continent)
3. if the client wants to screw me with litigation, I will not have the money to keep up the lawyer costs even if I'm in the right, my clients are typically MUCH bigger than I am
4. contract is unnecessary if delivery & payout cycles are small enough to limit risk exposure of all parties
5. the relationship has been arranged and agreed on through a Skype, meaning that any gross mishandling of the agreement (such as copyright issues) would still be covered via oral contract with physical proof of it happening (?)
6. just paying for a competent Croatian lawyer with US & Croatian contract experience to look at the contract proposal the client sent me will cost me a fortune

So the question, is the client really obliged by some aspect US law to sign a contract to continue working with me?

Note that the client cites anti-money laundry laws as the reason yet doesn't clarify which law exactly, but wouldn't proof of oral contract and a mountain of proof from code commit logs hosted on a tamper-proof third party cloud service be sufficient to cover this?

UPDATE 1

Now that I'm thinking about it, my arrangement with the client is quite a bit more complicated than the cookie cutter "you do work, we own software" agreement.

I gave them full rights to some of my software in exchange for full rights on some of the software I developed for them, so accepting a cookie-cutter contract would kind of be a bad thing for me, and would almost certainly open a 2-way litigation venue should any kind of conflict happen down the road, with a litigation-happy client especially - and me being very litigation unhappy on the other end.

That's why I'm asking if the contract is indeed necessary, because untangling which pieces of code are mine, which are shared, which are theirs, will be hard and expensive and would probably not be done 100% according to reality and open new pandora boxes, knowing lawyers and their level of software expertise.

On the other hand, a bunch of Skype chats is a helluva lot more unclear than a written contract, but a general understanding is that it generally carries a lot less weight too? (due to those same ambiguities)

Answer 1

You already have a contract(s): you do work and they pay you is pretty much all you need to have a contract. Given that there is already a contract, formalising it in writing does not expose you to any greater risk and usually, clearly defining the terms of a contract reduces risk all around.

Answer 2

I'm in the UK. In the same situation, the US company would receive bills from me, would pay the bills, would receive an acknowledgement that the bill is paid, and my (one man) company can be looked up on the Companies House website (https://www.gov.uk/government/organisations/companies-house) with enough details to show that it is a real company, paying real taxes on real income, and that I am personally behind it.

Assuming that they are saying the truth, all the contract needs to say is that you will be from time to time writing software for them, that you will be paid when the software is accepted, and that the software becomes their property upon payment. Nothing else is needed since you worked together well without a written contract.