I would have 2 sets of tweezers on the go if I was you ; Remove debris with surgical spirit and then pop into barbicide to complete the process.
One in sterilisation and one in use...... However I have 5 pairs of tweezers that I have to choose from for the various different jobs in the salon. So I never have to worry about the lack of sterilisation in barbicide.
Barbicide have special sized glass jars for small implements. well worthwhile getting to make you feel 100% happy about your tool hygiene.
For tweezers and nail tools I either wash them in soap and water or use a disinfecting wipe to remove debris, soak in Barbecide to disinfect, then I have a small glass bead steriliser to complete the process as although Barbecide reduces harmful micro organisms, its the sterilisation that totally kills microorganisms, bacteria and fungi. So spare sets like Rosie mentioned are definitely a good idea