All of the proposed options can all be performed without General anesthesia.
Some can be performed under local anesthesia alone with oral or intramuscular sedation, while other surgeons may prefer local anesthesia with IV sedation. This helps to avoid the general anesthesia which you have your reason for avoiding. Some people have a history or family history of Malignant hyperthermia from general anesthesia inhalational anesthetics (the anesthesia gases), which would be a contraindication for having general anesthesia.
I think a common element of all of your consultations is the necklift/submentoplasty.
I don't think that Botox on the platysma muscle bands does enough to flatten them out, and it is not a good long term solution. It can end up becoming a money pit, with less than optimal results.
The chin implant recommendation and necklift (submentoplasty/platysmaplasty) will both help with your neck profile. Redraping the neck skin will help slightly with skin texture from the mere repositioning of the neck skin, but these surgeries will have a very limited affect on the true texture of the skin. If you have significant sun damage and crepiness of the neck skin, the skin quality doesn't change with the surgical procedures.
I have heard good things with the fractional lasers, and I have seen patients treated by dermatologists in my area using Fraxel, with impressive results. I don't know how much of an improvement you will get on the neck skin, but it should change the texture since the laser is resurfacing the skin and not just repositioning it.
Profile versus Skin Texture
You mentioned two separate things about your neck which I consider different problems and the solutions are different. You mentioned mild to moderate neck laxity, which should mean some kind of hanging neck skin or neck bands (platysmal bands) which is making the neck skin hang by the tenting of the platysmal bands through the skin. In the end of your question your mention your "wrinkled neck" which suggests to me that you have more of a skin texture problem.
The submentoplasty is a mini-necklift with an incision solely under the chin, to lipsuction fat and tie together the muscle bands (platysmal bands) and sometimes also cut the edge of the muscle. A full necklift is the submentoplasty with additional incisions around the base of the earlobes and back of the ear into the hairline. A lower face and necklift will have incisions both in front and behind the ear.
By sculpting the profile of the neck on a fat and muscle level allows the neck skin can be redraped or repositioned into the "crotch" of the neck where the neck and chin meet. This angle is called the cervicomental angle (cervico- means neck; mental means chin). If the neck skin is wrinkly, you may see a slight improvement in the wrinkles when the skin is redraped into this cervicomental angle. When you have the "honeymoon swelling" everything will look great, but when the swelling is finally gone, you will still see some improvement, but not as much as during the "honeymoon."
The question you have to ask yourself is whether you are looking for profile improvement, or skin texture improvement. In general, profile improvement is performed using surgery and implants while skin texture improvement is a resurfacing procedure which involves lasers or peels. If both aren't bad, but you want improvement in both, you may opt for a combination procedure.
I hope this makes some sense.