Elective surgery with iv sedation but have Chronic venous insufficiency

Hello, I am a 25 year old male, non smoker, physically fit/active, 5'10'' 156 lbs. I am booked to have elective surgery to remove a mild case of gynecomastia (breast tissue) at a cosmetic surgery clinic in Brussels (I live in UK). The operation will last no more than an hour and I will be administered local anaesthesia with IV sedation. In addition to this embarrassing problem I've lately developed varicose veins on my legs. I’ve been diagnosed by doctors in the UK as having "Chronic venous insufficiency", more about this shortly.  My question is; Will this venous insufficiency create a potential danger to my life or well being whilst under IV sedation? I am worried about this but don't want to make an issue with the clinic (ie, tell them about venous insufficiency) as they might decide not to treat me if there is a small risk. Any input would be much appreciated, thanks!

Supporting information/symptoms:
LEGS- varicose veins starting to form though not yet tortuous. Pain when standing and a feeling of pressure and discomfort when sitting. Drinking even medium level of alcohol causes pins and needles type feeling in legs, this I fear might be a problem when I have sedatives coursing through my veins?
ARMS- pronounced/swollen arm veins, soreness in arms when arms are kept at my side for long periods, particularly in warm temperatures. Soreness is alleviated when I raise my arms higher than my heart.
In both legs and arms the symptoms have developed relatively quickly, really in the last 6 months. I've had smaller spider veins in my legs since I was 19 though.
BLOOD TESTS (nothing outstanding) Hormones: Serum oestradiol levels normal-160 pmol/L. Serum testosterone on the higher range of normal – 30.8 nmol/L

I've had gynecomastia breast tissue since adolescence when I was overweight. I have since lost the weight but have never been able to loose the last little bit as there is breast tissue present which needs to be excised.