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Just to add in, canned foam is probably rather sterile. While a puck and brush is exposed to the air constantly and wet or humid for quite awhile.
If the razor opens skin enough to cause small...

Ive never used this but it looks like it would work well.

Thayers Medicated Superhazel with Aloe Vera Formula Astringent - $9.95 : Thayers Natural Remedies, Since 1847