@biokult it's more than just the security situation that is raising red flags here. Your quotes have included:
"I think things have fallen through the cracks because of staff sickness.

They have a great HR department etc who I'm sure would help, but the problem is this has all be sprung upon me, and I need to really talk to my LM before escalating when I have just started.
....
So to be clear, my line manager is the one who didn't mention this [risk assessment].


It only came up when I was liasing with travel company they use. I then asked our HR department who said that categorically yes one was needed.
....
I haven't had a zoom/face to face meeting with anyone.
....
The thing that is confusing me, and what seems to go against what other have said is normal practise, is HR told me to do the risk assessment & mitigation procedures myself.

Obviously I'm not an expert, and it would be down to my line manager to advise, and given that she hadn't even mentioned a risk assemment would need to be done, I'm concerned they won't take it as seriously as they should.
It sounds like your line manager is not concerning herself with the very real risks to your security, you're not engaging with the correct level of HR to tackle the planning for this trip, and you are at greatest risk of people who haven't grasped the enormity of the suggested situation making decisions they are not informed about. People make crap decisions when they are not fully informed.
DO NOT ALLOW THIS TO HAPPEN!
That said, it also sounds very early in the whole process, so keep calm and diplomatic as you have been, but do prepare well for your first proper discussion about it on Friday! This should include questions like:
• Who was the last UK colleague who travelled to the main site in Mexico?
• When was that, did they travel solo or in a pair, and can you see the risk assessments and travel arrangements made for that trip?
• Who was the last UK colleague who did any visits OFF the main Mexico site? Ditto arrangements for that.
• Where is the highest risk location any UK colleague has travelled to globally, who in HR did the risk assessments, which external security advisor handled the transfer and local security arrangements?
• Where is the highest risk location your line manager has travelled to globally while working for your current employer? (This may lead to a good conversation with your LM, or it may be illuminating that she has NEVER undertaken work travel of this kind of risk she is proposing you undertake for her team!)
I think you have interpreted from an email that HR is suggesting you prepare your own risk assessment for this trip. I hope this is crossed wires! You should not be undertaking a trip to a neighbourhood of the nature you describe (FCO off limits, carjacking, sexual assaults, kidnap risk) without input from international security advisors who are professionals that provide security of the level other posters have referred to: pre-travel hostile environment training/armoured cars/armed drivers/bodyguards etc.
Do not let your line manager's naïvety about proposing this "site visit" put you as personal risk. Equally, stay diplomatic, ask well informed & prepared questions, and do not hesitate to escalate to an appropriate level in tour central HR team, and your career can fly!
You might end up not going to the "off" site, you may end up visiting & having great engagement, but being ferried there in an appropriately secure manner for the local risks.
You could always suggest that your line manager makes the trip with you, to gauge her comfort level about the safety procedures in place ;D
Good luck 