Will using higher wattage chargers degrade iPhone battery more quickly?
No.
The power rating of a charger has no bearing on the life of the battery nor the consumption of power by the device.  A higher wattage charger only means it can supply up to the specified amount of current, not that it will push that amount of current to the device.
Current is drawn, not pushed.
Regardless if this is an &quot;intelligent&quot; charger like a USB charger that conforms to the Power Delivery specification (USB-3.1 or higher) or an &quot;old fashioned&quot; charger, it's the device that draws the current from the adapter.
Chargers and power adapters are rated in watts which are calculated by multiplying the voltage (how much) by amperage (how strong).

For instance, a &quot;quick charge&quot; USB phone charger charger outputs 5V @ 2.4A, or 12W.  If you use a laptop charger like the USB-C charger for the MacBook Pro rated at 96W, it will only draw 12W of current because that's all the phone can pull.  However, if you connect the same phone rated at 12W and connect it to a charger that only supplies 5W, either it will charge slowly or it may damage your charger and possibly your phone.
This is where the &quot;intelligence&quot; comes with with respect to USB-C and Power Delivery.  The new USB-C chargers will negotiate with the devices as to what can be supplied.  In the simpliest sense, the device &quot;asks&quot; for power and the charger &quot;responds&quot; with what it can deliver.  This way, the device won't draw more than the charger can supply.
On the old fashioned devices (non-intelligent), there's no negotiation.  The device will attempt to draw the power it needs.  If the charger has the appropriate capacity, it will supply it.  If it doesn't it might pull more current than it can handle, potentially burning up the charger and/or damaging the device itself.
Further Reading
Various forms of this question has been asked previously.  Below is a small sampling for additional reading.

Is the Macbook 12 inch&#39;s USB-C charger interchangeable with other USB-C chargers or devices?
12V - 0,67 A USB Wall Charger for iPod Classic
Can I charge my headphones with the MacBook 12&quot; charger?
Other than speed, is there a reason that a 10W iPad charger shouldn&#39;t charge a new MacBook Pro 2016?
Danger of damaging 13&quot; macbook pro by charging it with 85w charger?