You can use the fungal bit of same diameter using cork borer (steel or brass). You can have this from your local glassware provider. It comes in different diameter such as 4 mm, 6, 8 10 mm depending upon the requirement.
Depending on your volume and how profuse your mycelial growth is, I would tend to go for about 1% w/w after growing the fungus on exactly the same media you are transferring to. To cover my bases, I'd also do a dry weight analysis and construct a standard curve (of a series of weights plugs at a specific time) so you can state with confidence (ie journal papers) the exact weight you have added for any experiment.
Obviously, you do not want your inoculum to be at the top of the growth curve when you inoculate (ie optimal but not peak biomass levels), then you'd have the complications of secondary metabolism and a slower growth respose of your inoculum as it kicks back into its growing phase. Always grow your inoculum under the same conditions that you are performing your solid-state fermentation on the medium you are transferring it to and always double or even triple wash to ensure no nutrient carryover. Also, make sure you take your inoculum from the leading edge, since this is where you still have active growth. ie standardise your methodology as much as you can.