Will I have a bad scar after conventional surgery to remove a 4mm basel cell carcinoma from the tip of my nose?

Depends on surgeon. First thing you want to do is to have the tumor completely removed. The way to ensure this is to have mohs micrographic surgery (www.Skincancermohssurgery.Org). Mohs surgery is skin sparing surgery with the highest cure rate (99%). The surgeon will check all the surgical margins to ensure that all the roots have been removed & then will repair the defect in a way which minimizes scar the same day.
Not necessarily. Basal cell cancers do not require a large margin of normal tissue when they are removed. A good plastic surgeon or facial plastic surgeon should be able to remove the cancer completely and create a scar that, in time, should be very inobtrusive. It will take about a year for the scar to fully mature, however.
Small lesion. Talk with surgeon. Small lesion with margin may b easy to take off with minimal cosmetic issues. Cure rate should b >95% with surgery but some risk of scars and defects. Radiation has 5% lower cure rate but no risk of scarring or dramatic cosmetic defect. Discuss with your dermatologist.
Could consider Xrt. The tip of the nose can b difficult to remove a cancer from without significant cosmetic detriments. Depending in the size of the lesion, a surgeon, either with mohs or other techniques can not entirely predict how large the defect would be until they attempt removal. Nasal ala and tip as well as parts of eyes and ears can b cured with electron beam radiation usually with low cosmetic damage.
Depends. If you are concerned about the size of the scar, it is essential that you have the tumor removed by a mohs surgeon. This will ensure that the entire tumor is removed while at the same time only removing what is absolutely necessary. Other surgical approaches will require taking a larger margin of tissue and will be sent to routine pathology which doesn't assess the entire margin.
Unlikely. You will have a scar as the tissue is shallow in this location, but techniques to minimize this are known. Discuss this with your surgeon. The earlier a basal cell is removed, the better.