You are correct, the 'offical' size of hole for M10 T-nuts is 13mm diameter which leaves a small space around the shaft for ease of fitting and to accomodate various tollerance factors such as the expansion of the metal, the effect on the surrounding wood of the prongs, manufacturing tollerances and the radius near the flange of the T nut etc. However for a climbing wall a 13mm hole may not be ideal because of the nature of the forces involved.
The strength of these fittings is primarily the 'pinching effect' of the sandwiching the mounting wood between the flange of the T nut and the flat back of the climbing hold on the other side. However since many of the forces in climbing are perpendicular to the direction of the hole there is some merit in getting the hole as tight as reasonably practical to reduce the induced turning moments when pulling or stepping on a hold that might possibly work the nut loose over time.
The actual outside diameter of the shaft is 11mm but this widens sightly near the flange so depending on the resilience of the wood you are attaching to, the accuracy of the drill bit and how tight a fit you are looking to achieve it is possible to use a smaller diameter: an 11-12mm drill bit may be sufficient to give a good tight sliding fit without using excess force. In very hard wood it may be necessary to chamfer the edge of the hole very slightly with a countersink bit to accommodate the flange radius although usually once the bolt is tightened it should pull the nut fully into position.
Finally, ensure you use a wood drill bit with light pressure to drill the holes to get a properly circular and parallel sided hole without causing splintering. The most common drill bits found in tool boxes are general purpose HSS (high speed steel) bits but these do not create particularly accurate holes in wood, particularly larger sizes tend to create slightly triangular shaped holes and create splinters which damage the surface when they exit the other side of the workpiece.
We have seen some climbing wall instructions advocate the use of a 10mm hole. In our opinion this would likely damage the integrity of the wood around the hole during the insertion process which would inevitably require great force and so the damage would actually reduce the longer term effectiveness of a tight fit rather than improve it; it may even damage or distort the T-nut in extreme circumstances.
