Can I remove the Hydration shortcut and replace it with a BP shortcut? I have never used or entered hydration data but track my Blood Pressure daily…

Ah, OK, I misread your original post - for some reason I saw "I do not have the Index BPM". Well, it is a bit paradoxical that you need the device for being able to enter the BP manually. It…
A solution might be borrowing the Index BPM from someone, or doing a test purchase, adding it to GC and then returning - you'd keep the possibility to enter the BP manually
Just change the country to USA in your Garmin Profile at https://www.garmin.com/account/profile/ - it works fine, tested.
... however, the blue Activity / Weight / Hydration selection for adding data cannot be modified. You can only remove the entire Hydration panel, not the blue buton from that tool. The blood pressure can be only entered automatically from a Garmin Device (currently only the Garmin Index BPM Smart Blood Pressure Monitor). AFAIK, you cannot enter the BP manually. You could only import the BP data if you managed to replicate the internal FIT files used by the Index BPM device.
Ah, OK, I misread your original post - for some reason I saw "I do not have the Index BPM". Well, it is a bit paradoxical that you need the device for being able to enter the BP manually. It does not make much sense. But then, it is not unusual with GC. And in fact my original advice telling that for the BP you need the Index BPM device, or replicating its FIT files, stil stands.
I assume you also don't have access here: https://connect.garmin.com/modern/blood-pressure