If you have to fudge LMP date (like PPs, I wouldn't feel comfortable having to be dishonest about it), maybe pick 10 days after your real LMP. That should at least get you O'ing 14 days prior to expected AF in a 38 day cycle, and if you O later than that, it's only off by a couple days probably.
I have 35 day cycles and O around day 23. The NURSE is married to the wheel, but thankfully, my OB actually listened to me and told me to schedule the dating u/s for later than normal, so I'd be closer to 8 weeks preg at the time of the u/s. Due to the OB being out of town that week, I had to go the week before, so I ended up being 7w1d (by my own estimate) at the time of u/s. The u/s dated me at 7w2d-7w4d, so they took the average and said I was 7w3d and put my due date in my chart based off that. So it's 2 days off what I tell everyone, but not a significant enough difference.
If you tell your OB that you don't know your LMP, they'd probably do a dating u/s (which insurance should cover in that case), and they are pretty accurate early on (like 8-10 weeks). They get inaccurate later, especially as you get into the 3rd trimester (my DS was measuring 31 weeks at 29 weeks, but thankfully, I charted and knew how far along he was - it made a difference as to how he was treated in the NICU).
The funny thing is... both pregnancies, when I've talked due dates with my midwife, she's picked up the wheel, and I told her to put it down. She did.
I chart and know when things happen, so the wheel is not helpful at all.