I've used a 6 cell D-cell battery holder for cheap isolated powering of 9V equipment for long periods. You can get them on eBay or Amazon for about $5.
There are 4 advantages to doing this.
1) Alkaline D-cells are relatively cheap.
2) They can be used for lot's of other household things, like flashlights, toys, etc. So won't go to waste before they are depleted.
3) Being external, if they leak they will not destroy your meter.
4) They pack a lot of energy. They will likely power a UT61E for many, many months.