In the nicest possible way, it is not simply as easy as saying find someone understanding to do a smear test. PTSD is an extremely complex thing, when mine was at its worst I went into cardiac arrest a few times from trigger induced stress. Now, admittedly I do have heart problems, but PTSD can have extreme effects on physical health, not just mental health.
Yes there's a risk involved in not going for a smear test, but if you do go you may be risking your PTSD being triggered. Many people do many risky things - smoking, driving, skiing etc. If the individual is capable of making an informed choice then their choice should be respected.
Trying to coerce someone into going for a smear test to me feels like someone trying to coerce me to allow my body to be subjected to something I don't want it to be, and that starts drawing nasty parallels.
To be frank even discussing smear tests makes me tense and grit my teeth, and its be quite a lot of years since I overcame my PTSD, I've had all the counselling under the sun and I'm as recovered as I'll ever be. That said, in truth I don't think anyone ever overcomes PTSD fully, its shadows stay with you forever, and however much you can overcome your responses to triggers, I still flinch involuntarily, or find myself irrationality, albeit mildly irked when I encounter what used to be a trigger.
I've known an awful lot of people with PTSD and I don't know a single one who has ever fully and completely overcome it, scars may heal but the marks stay.
OP - your body, your choice. If you don't want to have it done and the letters are making you feel stressed, go and fill out the form a PP mentioned and opt out. If you feel that in time its something you may feel able to consider then you can go to a sexual health clinic or similar, but in the meantime the lack of letters and HCPs mentioning it may help.
As a separate issue, if you haven't already counselling can really help, and hang in there, its a long hard road but it does get better, just take it one day at a time 