As OTM options get closer to ATM, their Vega will increase. However, they become less sensitive to changes in IV. So, assuming your puts are still relatively OTM, you could hedge your Vega exposure by selling some ATM options. If Vol were to drop, the (short)vega of these options would stay relatively stable.
You could structure it a few ways by;
-selling shorter duration
-selling a 1xN ratio, to create a cheap fly
-some combo of both
Or, you book some gains. Remember, the goal is to make money, not devise the perfect hedge. But, if the thesis of the trade is still in-tact, then you want to maintain your exposure, while reaping the reward of gamma.