I simply don't find any biblical basis against using birth control. Vasectomy is the cheapest and most effective form of birth control. It is probably also the safest, though I haven't seen any studies comparing it to long term use of birth control pills. It is also permanent, or at least should be considered so. Reversals are painful, expensive, not covered by insurance, and don't always work.
There are rare side effects, most of them mild and temporary (I sound like a commercial), check with your doctor

It is in general considered one of the simplest and safest operations there is.
I think the biggest issue is whether you are certain you will not desire children in the future. Obviously only you will know about that, though the fact that you are forty doesn't make me think you're likely to change your mind.
I had a Vasectomy at 26. I had no complications and have never regretted my decision for a single day.