Remove direct bitcoin calls from qt/sendcoinsdialog.cpp

Summary:
Partial backport of Core PR 10244
https://github.com/bitcoin/bitcoin/pull/10244/commits/56f33ca349b3721a15fce3bf0b6d4fd7fd788970
Progress towards T417
Depends on D2888

Test Plan:
make check
ninja check
bitcoin-qt # sanity checks on send coins dialog

Reviewers: deadalnix, Fabien, #bitcoin_abc

Reviewed By: Fabien, #bitcoin_abc

Differential Revision: https://reviews.bitcoinabc.org/D2889