A lot of sources on the Internet claim that fast charging immensely reduces your battery capacity over time. But you have to be careful interpreting them. For instance, take this figure:
As you can see charging at 2C ( = full charge within 30 minutes) reduces the battery capacity significantly. But charging at 1C doesn't seem to cause a lot of additional capacity degradation. I mean the degradation at normal charging rates is pretty close to that from my experience.
Honestly, I doubt that your charger would even charge at 1C (= full charge within 60 minutes). But even if it would be slightly above 1C you would probably be fine.
Unfortunately I couldn't find studies where charging rates below 1C where analyzed more closely.
If you want less capacity degradation you should avoid charging your battery at constant voltage. The constant voltage charging happens when it hits 4.2V-4.4. As the following figure shows, this is where most of the capacity degradation happens:
I can't tell you exactly at how much percent the constant voltage charging will kick in for your battery. It's probably at around 90%. So if you stop charging at that point. You should see less capacity degradation.
Very hight/low temperatures and very fast discharging will also degrade the capacity.
I recommend reading the following article:
You mention that charging from 0%-100% takes 1 hour 45 minutes. When your smartphone reports 0% battery the battery usually hit around 3V even though LiPos can safely be discharged to around 2.7V. (This is basically done to ensure a safe shut down.) So I would say your charger has a C-rate of about 0.5C. So you really shouldn't be able to notice any any additional capacity degradation.
And your suspicion about the trickle charging is probably right. As charging at constant voltage is significantly slower. So we can assume that your battery is being charged at constant voltage as soon as it its around 95%.
Conclusion: Only charge your battery until it hits 95% or maybe even better 94% and battery capacity degradation should be greatly reduced.