First, the idea that high cholesterol is unhealthy and a risk factor for cardiovascular disease is pretty much outdated if you look at the research these days. Associations were found but as any good doctor should know, associations don't prove causality. Also, findings were mixed and sometimes, NO association was found at all or the opposite. In recent years, the more important markers have been found to be HDL (oral estrogen increases it) and especially triglycerides...and blood pressure (bio-identical estrogen has been found to reduce it, as well as spironolactone). And glucose levels as well as HbA1c (non-oral estradiol improves insulin sensitivity). These matter much more. Do your research, and check out the site The International network of cholesterol skeptics. If anything, female HRT reduces your odds of getting any cardiovascular complications as estradiol promotes vasodilation of arteries and has a positive effect on your lipid profile RATIO (cholesterol:HDL, LDL:HDL).
Non-oral estradiol rarely, if ever, at doses prescribed for transwomen, raises cholesterol levels anyways or triglyceride levels because very little circulates through the liver. So, on non-oral, it shouldn't even be an issue. Estradiol also tends to lower LDL but as research has found in recent years, the LDL thing is more complex than we first thought and there are large particles of LDL and smaller ones. The latter have been found to be more atherogenic.
I'm on estrogen since 2004 and at times, my cholesterol levels have indeed gone up (more to do with eating habits than hormones) but so has my HDL so that my ratio remained perfect/ideal. Triglycerides have remained normal and the less carbs I ate, the lower they were. The reason my HDL is high is because I eat so much saturated fat.
Personally, I would never take statins as they are associated with several side-effects (muscle wasting/pain, memory troubles, mood problems, etc.) and I think that one can cut down their risks by simply eating healthier, exercising and taking the right sex hormones (bio-identical). Statins, in my non-professional opinion, have been overhyped so much so that the pharmaceutical companies are reaping the benefits and some people are suffering as a result.
In any case, I encourage everyone to be proactive in their lives and do their own research. You make your own conclusions and then you can discuss with your doctors, seek a second and third opinion. Etc.
Best of luck and I highly doubt you'll be refused. If you are, find another doctor who is competent in the matter.