Apart from speeding up your code, there are some other improvements possible that I don't see mentioned yet.

The speedup

As other users have already picked up, you only need to transform around 200 countries instead of 17k rows. You can do this efficiently by storing the mapping in a dictionary:

iso_map = {country: do_fuzzy_search(country) for country in df["Country"].unique()}
df["country_code"] = df["Country"].map(iso_map)

This is in essence very similar to using the lru_cache proposed by Peilonrayz, but it's a bit more explicit.

Consistent naming

As a side note, I would advise you to use a consistent naming scheme in your DataFrame. This doesn't have to follow the python convention, but it should be easy to remember.

For example, turn all columns to lowercase by using something like:

df = df.rename(columns = {name: name.lower() for name in df.columns}

Using categoricals

Since the number of countries (and isocodes) is limited, you might want to consider using categorical columns. These have the advantage of requiring less memory and being faster on some operations.

It might not be worth the extra lines of code in your situation, but it's something useful to keep in the back of your mind.