Hi Dougie,
On your existing mortgage interest at 5.8% on €77,000 is €4,466 pa. After tax relief on 75% of the interest (assuming a tax rate of 50%) the cost is €2,792.
If you could remortgage at 4% the interest would be €3,080 and after tax relief €€2,792.
This is a saving of €867 in the first year, the saving would be less each year as the capital reduced. In total I calculate the saving to be €3,034. This might not be worth the trouble and cost of remortgaging.
If you do not remortgage you should definitely overpay as much as possible. You will not get a guaranteed after tax return of 3.6% (€2,792/€77,000) anywhere else.