I've had both products at various points and would offer the following two pennies of advice.
1) Good for you, focussing on early payment of your mortgage - smartest thing anyone can do financially.
2) Offest mortgages are great if you have a chunk of savings and you want to keep it available, but they generally do not have the best interest rates. If you feel in any way insecure about your emploment, that of your partner, or chance of a big hidden cost suddenly arriving, then its good to have an offset, where your savings are working on the mortgage balance, but remain available.
3) A fixed rate or tracker may give you a better rate in the short term, but in order to have you savings reduce your mortgage balance, you'd need to commit the 20K at the point your remortgage. Whenever I've done spreadheets, this has been the better way to reduce th emonthly payment and overall amoutn paid back over th elifetime of the loan, BUT it does take away the flexibility of having that 20K for any unforseen problems.
Best of luck