I feel like a bit of a broken drum here but you don't need a secondary, and in woodland you'll rarely find a reason to use one (beyond "Want to"). I mean, assuming that your T10 shoots under your site limit for auto-guns, with the BB's that you intend to use (I'd suggest 0.28g+) which I did mention up-thread and I hope you've got an assurance from the seller on that.
What I run alongside a DMR or sniper is a light plastic MP5K on a leg panel with a 500 round high-cap magazine. Strap on and forget it, it's a full size AEG gearbox in a close-to-pistol-size frame, and actually lighter than a pistol + mags for even a fraction of that ammo capacity. Full sustainable auto, close to 1J, it's a compelling combination. I wouldn't want to carry anything bulkier than that as a secondary, and there shouldn't be any need to with a T10 primary. Having a backup gun with you is a good idea, but it doesn't need to be anything special given that you'll ideally not be using it.
For fun factor, gas blowback pistols are hard to beat, although I'd stress how little you'll likely use one in woodland at most sites. AAP-01, or Tokyo Marui Hi-Capa or G17 are common choices. As we're into Winterish weather, you could consider CO2 although I've never bothered because MP5K Master Race, and the risk of running too hot.