Use of Standardizer to handle outliers?
Standardising may not be the best option.

Because they will still not be bounded (like when normalised) between -1 and 1 but be distribution dependent. What I mean is if they are outliers their standard deviation will be big for these values. In any case its not that you should rescale the values to combat these outliers. Outliers are not in the first place problematic because they are big in values, but mostly because these values lie in the cluster thats not possible/representative of future data and you will learn on it.

One solution for without dropping them is for example binning, where you say all outliers that have standard deviation bigger than two should have value "X" where X is some 99,5% quantile for example.