No. Your board must approve "material" transactions (learn more here). The definition of material is fuzzy, but buying a software solution to manage your cap table is not an example.
Seeking board approval for something not required costs you legal fees in drafting the approval, wastes investor and board member time to review and sign off, and delays the process of onboarding your cap table.
In short, seeking board approval costs you time, money and forces key stakeholders like investors and board members to spend valuable time on something irrelevant to the core business of your company.