43-yr old female. Sore breasts and nipples. Period 6 days late. Husband has had a vasectomy. Could this be perimenopause symptom?

Yes. During the perimenopause your reproductive hormones fluctuate much more than previously. The highs and lows can lead to various symptoms including significant changes in the timing of your periods, breast tendernes, and others. Your gynecologist can help sort this out if you have continuing symptoms.
Likely pre-menopause. Logical possibilities are either pregnancy or pre-menopausal hormonal changes. Vasectomy is not a guarantee of sterilization, so a home pregnancy test would not be unreasonable. If a pregnancy test were to turn positive, then the husband should have a semen analysis to determine possible failure of the vasectomy.

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