Savage Worlds skills are intended to be broad, allowing characters to focus primarily on Edges for customization rather than multiple iterations of something like Fighting for edged weapons, Fighting for blunt weapons, etc.
If it's important to your setting to have more detail, a character uses his normal skill for one device of choice. When using any other variation he suffers a -2 penalty.
Gaining an additional specialization counts as raising a skill below its linked Attribute. So a character can gain two new specializations with an Advance, or gain a specialization and increase a skill below its linked Attribute.
Below are skills appropriate for this extra detail and some example specializations:
Savage Worlds Deluxe Edition p. 110