If you were already on your company HSA making contributions, those funds are yours and you can spend them or potentially "roll" them into your 401(k) (I don't recommend this, as this is not a qualified HSA expense!). Talk to your plan administrator. You probably need to be on your employers plan to continue contributing, however.
You can have more than one health insurance plan covering you. Carefully consider:
So, you'd be on two plans, potentially paying two premiums and would have to think about two deductibles, out-of-pocket maximums, and so forth.
You also have this concept of primary and secondary coverage. You don't get to pick which is which. If you're on your companies HSA, that's your primary coverage, and your spouses plan counts as secondary. This means when you file your claim, it goes on your primary insurance plan. Anything not covered by the primary can potentially get covered by the secondary plan, but the initial claim does not go toward the deductible of your spouses plan.
I think that many HSA plans are "high" deductible plans. So this decision may come off as financially riskier.