You need the terms and conditions. What you can do though is simply changes the specs of the terms and conditions to accomodate this segment of your clients.
People who want the license but are willing ( for whaterver reason ) willing to aquire the product on their own dime can still do so. Protect yourself by having the typical "if purhased your agreement of terms and conditions is implied..." With that said is always best if you make them read them... Such as if digital, form is cannot be acknowledged unless they open the terms and conditions form or scroll through it. That way is more alwyas more on them than your company.

We cant ever avoid a lawsuit or allegations but what we can do is simply allow people to make their educated decisions and us record such acknowledgement of information.

I read and re-read your question and I'm not sure I understood the situation. If they issue a purchase order

The short answer is that you need a business attorney to help you here. Yes, they are expensive. But in the long run, hiring an attorney will save you time and money while avoiding unnecessary problems.

If the company isn't going to sign the contract ever then what it is that they want you to sign? Is the company asking you to sign their version of terms & conditions? If yes, then you need to be a bit cautious in terms of reading between and behind the lines.

I don't get it when you say "Several staff members of the companies want to avoid their legal department". Are you trying to sell to individuals in an organization apart from organization itself?

Looking for any specific input? Do feel free to reach out.

I work in the public sector, and in my experience terms and conditions still bear culpability. If your clients want you to sign their PO because they don't want to deal with contracts and their legal team, and it has terms and conditions, then I would consult your leadership or legal team. Maybe one of them could sign it.

At the same time, even though the contract process is a little laborious, it may be worth it to prevent redoing things every year. You could ask you clients if they have a standard purchasing agreement that you could sign (pending your organization is OK with it). That makes the process usually pretty speedy.

I always focus on the customer experience. I also focus on culpability. Therefore, my happy medium is usually to communicate how valuable our clients are to us, but that a contract is the more secure, and convenient option (especially since you have licensing renewal requirements annually). And then I do everything I can to make the process easy for them.

-Diane