Short version: yes, the plane can take it
The 737 — or any other plane — will not take off unless the wind is within safe limits for the aircraft type.
Long version: your question almost answered itself
Did you know that last year there was not even not one single airfare-paying passenger fatality? Keep this in mind for a while...
Now, you came here asking "Are these wind speeds within the safe limits of this aircraft type?" There are two answers to this: "Yes", or "No".
I want you to ponder the potential answer: "No, those wind speeds are not safe for the 737 to fly in, but they keep doing it anyway". Does that sound like a realistic answer to you? Do you honestly believe that this is the way flight operations are being conducted across the world? When reading it like this, I do not think that this is what you believe, am I right?
But let us toy with the idea for a while anyway. Assume this is true. What would that mean? Well if this was the case — that aircraft are permitted to take off in wind speeds they cannot really handle — you would be hearing about a lot more crashes than you do. Planes would be dropping to the ground left and right. It is inevitably so that — if the answer was that planes fly in winds they cannot handle — there would be more crashes.
But this is not something you hear about, because it does not happen: planes do not take off in winds they are not certified to be able to handle. Last year's record — with not a single fare-paying fatality — would not be possible if planes were allowed to take off into dangerous winds.
So it does not really matter what the weather prognosis says, because if — on the day of your travel — the winds are more than the plane can take, the flight will be cancelled.
This is not even mentioning the fact that the limits imposed on aircraft have a safety margin built into, so that even if winds do gust up a little bit more, the plane can still take it.
And if the weather at your destination has fouled up before you get there, well this is what the divert airport is for. The divert is a pre-planned backup airport that the flight can go to if things turn fouler than expected.
So in the end: yes, your plane will be able to take the winds that prevail on the day of your flight, guaranteed, because if there are worse winds than that, you will not be flying that day.