Code

example:

import pandas as pd
import numpy as np

column_original = [1, 2, np.nan, 6, 8, np.nan]
df = pd.DataFrame(column_original, columns=['column_original'])

df:

   column_original
0              1.0
1              2.0
2              NaN
3              6.0
4              8.0
5              NaN

convert values ​from a column to int and str, without converting null values

cond = df['column_original'].isna()
s = df['column_original'].astype('Int64').astype('str')
df['column_original'] = df['column_original'].where(cond, s)

df:

  column_original
0               1
1               2
2             NaN
3               6
4               8
5             NaN

checking result

for i in df['column_original']:
    print(i, type(i), pd.isna(i))

print:

1 <class 'str'> False
2 <class 'str'> False
nan <class 'float'> True
6 <class 'str'> False
8 <class 'str'> False
nan <class 'float'> True

If your starting point is the data itself (i.e. the list column_original), rather than a df already containing it, you can accomplish the desired result using pd.DataFrame and passing a pd.Series with dtype=str:

import pandas as pd
import numpy as np
    
column_original = [1, 2, np.nan, 6, 8, np.nan]

data = {'float': column_original,
        'object': pd.Series(column_original, dtype=str)}

df = pd.DataFrame(data)

Output:

df

   float object
0    1.0      1
1    2.0      2
2    NaN    NaN
3    6.0      6
4    8.0      8
5    NaN    NaN

df.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 6 entries, 0 to 5
Data columns (total 2 columns):
 #   Column  Non-Null Count  Dtype  
---  ------  --------------  -----  
 0   float   4 non-null      float64
 1   object  4 non-null      object 
dtypes: float64(1), object(1)
memory usage: 224.0+ bytes

for col in df:
    print(f"{col}, values: {df[col].tolist()}")
    
float, values: [1.0, 2.0, nan, 6.0, 8.0, nan]
object, values: ['1', '2', nan, '6', '8', nan]

Note: you can also set dtype=str inside pd.DataFrame, but that will affect all columns:

pd.DataFrame(data, dtype=str).dtypes

float     object
object    object
dtype: object

Of course, if you start with the df, but still have the list as well, you can also overwrite the data in a similar way:

column_original = [1, 2, np.nan, 6, 8, np.nan]
df = pd.DataFrame(column_original, columns=['column_original'])
df = df.assign(column_original=pd.Series(column_original, dtype=str))

df['column_original'].tolist()
# ['1', '2', nan, '6', '8', nan]

Explanation: When you are converting it to str then nan -> 'nan' will become string, so in the apply function instead of using this lambda expression, lambda x: np.nan if x is np.nan else x use this, lambda x: np.nan if x == 'nan' else x

IPython code :

import pandas as pd
import numpy as np

column_original = [1.0, 2.0, np.nan, 6.0, 8.0, np.nan]
df = pd.DataFrame(column_original, columns=['column_original'])
str_df = df.astype('str').apply(lambda x: np.nan if x == 'nan' else x)

# You can verify it with .isna() function.
str_df.isna()

Output:

0    False
1    False
2     True
3    False
4    False
5     True
Name: column_original, dtype: bool

Also from here, is an apt statement regarding when to use is and ==,

Use is when you want to check against an object’s identity (e.g. checking to see if var is None). Use == when you want to check equality (e.g. Is var equal to 3?).

Edit:

After reading @ouroboros1 answer, I want to simplify my answer to just two cases (explanation remains the same),

1. If you want pandas Series object or pythons List

column_original = [1, 2, Nan, 6, 8, NaN]
series = pd.Series(column_original, dtype=str)
pylist = pd.Series(column_original, dtype=str).tolist()

2. If you want pandas DataFrame object

column_original = [1, 2, Nan, 6, 8, NaN]
df =  pd.DataFrame(column_original, columns=['column_original'], dtype = 'str')

Hope it helps.