Wide shelling does not increase the damage of Wyrmstake. Wyrmstake's damage scales with shell level and weapon damage on the repeated hits, and deals a flat raw damage based on shell level on the final hit. Since the highest shelling level is on Normal gunlances, those will deal the most damage with Wyrmstake.
Wyvernstake Blast is a weird one. The initial injection scales with weapon damage, but the detonate damage has weird interactions with the shelling types and different kind of firing. For example, a Wide Lv4's shelling deals 43 damage on its own, and detonates Wyvernstake for 22, while the shells from its full burst deal only 39 each. but detonate Wyvernstake for 36 damage.
By comparison, a Normal lv4 shell deals 22 and detonates for 12, while its full burst shells each deal 26 damage and detonate it for 20 each.
Looking at charge shots, Long Lv4 deals 73 but only detonates WSB for 54, while Wide4 deals 59 and detonates for /66/.
Wide4 actually detonates for the same damage with its normal shells and charged ones as Normal Lv5 does (22/66), but this doesn't scale directly. Wide5 detonates for more than Norm6 -- 32/96 for normal/charged shelling, vs Norm6's 26/78.
The move is an absolute headache to calculate.