Improve scikit-learn Logistic Regression model vs Statsmodels – significant variables

I’m working on an binary classification prediction and using a Logistic Regression.

I know with statsmodels, it is possible to know the significant variables thanks to the p-value and remove the no significant ones to have a more performant model.

import statsmodels.api as sm
# Add a constant to get an intercept
X_train_std_sm = sm.add_constant(X_train_std)
# Fit the model
log_reg = sm.Logit(y_train, X_train_std_sm).fit()
# show results
log_reg.summary()

Logit Regression Results Dep. Variable:     y   No. Observations:   1050
Model:  Logit                           Df Residuals:   1043
Method:     MLE                         Df Model:   6
Date:   Wed, 17 Aug 2022                Pseudo R-squ.:  0.9562
Time:   13:26:12                        Log-Likelihood:     -29.285
converged:  True                        LL-Null:    -668.34
Covariance Type:    nonrobust           LLR p-value:    5.935e-273
        coef        std err     z   P>|z|   [0.025  0.975]
const   1.9836      0.422   4.699   0.000   1.156   2.811
x1      0.1071      0.414   0.259   0.796   -0.704  0.918
x2      -0.4270     0.395   -1.082  0.279   -1.200  0.346
x3      -0.7979     0.496   -1.610  0.107   -1.769  0.173
x4      -3.5670     0.702   -5.085  0.000   -4.942  -2.192
x5      -2.1548     0.608   -3.542  0.000   -3.347  -0.962
x6      5.4692      0.929   5.885   0.000   3.648   7.291

In this case with statsmodels, I should remove 3 of my 6 variables the keep only the significant ones and then reload the model.

Is it possible to do the same with sklearn? How to know the variables to remove if p-value >5%? How to improve the logistic regression model performance with Sklearn? Do I need to implement a statsmodels and then use the correct variable to go with a model using Sklearn ?

Here my code:

from sklearn.model_selection import train_test_split
from sklearn import preprocessing
from sklearn.linear_model import LogisticRegression
from sklearn import metrics

#transform data
y = df.is_genuine.values
X = df[df.columns[1:]].values
X_name = df[df.columns[1:]].columns

# split data
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=42, stratify=y)

#standardize data
std_scale = preprocessing.StandardScaler().fit(X_train)
# transform X data to fit the Scaler
X_train_std = std_scale.transform(X_train)
X_test_std = std_scale.transform(X_test)

#logistic regression
reg_log = LogisticRegression(penalty='none', solver='newton-cg')
reg_log.fit(X_train_std, y_train)

#model training performance
reg_log.score(X_train_std, y_train)
>>> 0.9914285714285714

#model prediction
y_pred = reg_log.predict(X_test_std)

#test the model
pred = pd.DataFrame(X_test_std, columns=X_name)
pred['is_genuine'] =  y_test
pred['pred_reglog'] =  y_pred
pred['is_genuine_reglog'] = pred['pred_reglog'].apply(lambda x: True if x >0 else False)

# model evaluation
print (metrics.accuracy_score(y_test, y_pred))
>>> 0.9888888888888889