I agree with Dr. Landi; See a vein specialists for an evaluation and duplex US. Based on the findings a comprehensive plan should be made which may include various modalities mentioned on this thread.
The appearance of spider veins can occur as an isolated issue but on the other hand can signal a more significant underlying vein problem. Start out with an evaluation with a physician who specializes the treatment of vein disease (phlebologist, surgeon, dermatologist). A part of your evaluation should include a duplex ultrasound exam to determine the function of both your deep and superficial veins. The best treatment can then be recommended for you.
From you details it seems that Temporal Arteritis has been ruled out in your case. Was this eliminate by you having a negative temporal artery biopsy? It is very important that this is absolutely ruled out since it left untreated can lead to significant problems with your vision in the future.I agree with the previous comment that it is unlikely that a surgeon will remove a normal temporal artery....see a vascular surgeon for a consult.
I prefer the Aura 1064 laser for spider veins on the nose. With the cryogen spay it practically painless and gets good resolution of these type veins. Additional treatments will most likely be need in the future.