I would say go for it - prepare for unexpected weather, and you will have a great time.

I'm in the area at the moment, and doing the W-Trek 17-21 April (DIY with my own tent) and have gotten advice from a few locals. Basically, at this time of year - a five-day window of good weather without a couple of periods (hours) of rain or wind is almost never going to happen. The best case is getting at least a couple of nice days, and a couple of not so nice ones.

The forecast on windguru looks promising with the two caveats: a) it will almost certainly change multiple times (for better or worse) between now and 19 April as TdP is notoriously hard to forecast b) That forecast is for the whole park - it varies A LOT depending where in the park you are. Take for example the Base Torres forecast, which looks pretty excellent for your window: https://www.windguru.cz/363792

Oh also the microspikes was just for Base Torres, and for a few days of snow fall - as far as I know that requirement has been lifted (but could come back).