10mm is such a small amount infill off any amount will still need sealing so perhaps a 11.5mm bit off ply[called 1/2 inch] 3mm below surface and a bead off silicon to fill in will be less obvious
then if that fails another option can be looked at with minimum effort
in this instance affixed to the worktop back edge for security
what colour is the worktop the tiles and the grout ??
"simplesteve" already seems to have covered this